User:Charles Matthews/red links

• Wikipedia:Requested articles/mathematics

• http://www-gap.dcs.st-and.ac.uk/~history/Indexes/Full_Alph.html

Contents: Top - 0-9 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

My missing links:

A

Artin's approximation theorem - algebraic space - Azumaya algebra - N. C. Ankeny - absolute Hodge cycle- algebraic differential equation - Anabelian geometry - Ancillarity - Arithmetical algebraic geometry - Ascending Kleene chain - Analytic class number formula - Arakelov theory - Abelian sum - Acyclic covering - Adjunction formula (algebraic geometry) - Albanese map - Alexander duality - Algebraic de Rham theorem - Algebraic equivalence of divisors - Approximative point-spectrum - Affine Weyl group - Alcove - Associated curve - Associated line bundle - Atiyah-Bott formula -

B

Bryan Birch - Borel-Moore homology theory - Bott-Duffin theorem - Baker's method - birationally equivalent - Bombieri's theorem - Banach's theorem - Base locus - Beez theorem - Bernstein inequality - Bernstein's theorem - Beurling algebra - Beurling's theorem - Bicharacteristic - Bieberbach's inequality - Bieberbach's theorem (complex analysis) - Bieberbach's theorem (group theory) - Birational invariant - Birational map - Bitangent - Bitrace - Bitype - Bochner-Godement theorem - Bochner-Martinelli formula - Bochner-Yano theorem - Bockstein homomorphism - Bohl's theorem - Bonnesen inequality - Bonnet theorem - Bony theorem - - Borel conjugacy theorem - Bott formula - Bott residue formula - Bott theorem - Branch locus - Branched covering - Brunn-Minkowski inequality

C

classification of algebraic surfaces - Crystalline cohomology - completely reducible - contact transformation - Cartan-Kähler theorem - Chern-Weil theory - Calderon operator - Calderon-Vaillancourt theorem - Canonical curve - Cap product - Carleman kernel - Carleman's criterion - Carleman's inequality - Carleman transform - Cartan conjugacy theorem - Cartan criterion - Cartan-Kuranishi theorem - Cartan subgroup - Casson invariant - Castelnuovo curve - Castelnuovo-de Franchis theorem - Castelnuovo-Enriques theorem - Castelnuovo lemma - Cauchy characteristic vector - Cauchy data - Cauchy formula for convex bodies - Cauchy kernel - Cayley-Bacharach property - Cayley-Brill formula - Chern-Lashof theorem - Chevalley basis - Chevalley theorem - Chordal variety - Christoffel-Darboux formula - Classification theorem for algebraic surfaces - Clifford's theorem - Closed unbounded operator - Coercive form - Cohn-Vossen theorem - Complete maximum principle - Compressible mapping - Condensation of singularities - Conormal bundle - Contingent (mathematics) - Continuity principle - Coincident point - Cotlar-Knapp-Stein lemma - Cotlar's lemma - Coxeter element - Coxeter number - Cremona transformation - Crofton formula - Current (mathematics) - Cuspidal point of a surface - Cut locus - Crystalline cohomology

D

different ideal - dilation theory - double point - D-module - Darboux theorem - Defect of an unbounded operator - Deficiency of a linear system - Degree of an algebraic variety - Denjoy-Carleman theorem - Denjoy-Luzin theorem - Differential ideal - Direct image sheaf - Directrix of rational normal scroll - Dirichlet algebra - Dirichlet norm - Dissipative operator - Divisor with normal crossings - Dixmier-Kirillov theorem - Dolbeault cohomology - Dolbeault complex - Dolbeault theorem - Dominant weight - Double curve of an algebraic surface - Dual abelian variety - Dual curve - Dual Kummer surface - Dual Schubert cycle - Dehn-Nielsen theorem - Dehn's algorithm - Dehn's lemma

E

enumerative geometry - étale morphism - explicit formula (L-function) - Eikonal equation - Elementary solution - Elliptic complex - Elliptic surface - Engel theorem - Enriques classification of algebraic surfaces - Enriques-Petri theorem - Enriques surface - Enriques theorem - Equi-integrable set - Equirepartioned sequence - Essentially self-adjoint bounded operator - Euler class - Euler sequence - Exceptional divisor - Ext functor of sheaves - Exterior function - Extremal point -

F

Fubini-Study metric - Formal scheme - flat cohomology - Fredholm determinant - Factor set - fixed field - Fredholm theory - Fabricius-Bjerre-Halpern theorem - Fary-Milnor theorem - Fenchel inquality - Fermat surface - Fine sheaf - Fischer-Riesz theorem - Flat vector bundle - Flex point - Flight vector - Friedrichs theorem - Fröhlicher-Nijenhuis theorem - Fröhlicher relation - Fröhlicher spectral sequence - Fundamental weight -

G

Grothendieck category - generalised eigenfunction - Garding-Browder theorem - Garding integral - Garding inequality - Garding-Vishik theorem - Gelfand pair - Gelfand transformation - General type - Geometric genus - Giambelli formula - Gleason part - Gleason-Yamabe theorem - Global duality theorem - Godeaux surface - Green kernel - Group with no small subgroups - Gysin sequence -

H

holomorphic line bundle - Hereditary ring - Hilbert modular form - Height function - holonomic system - Hadamard-Cartan theorem - Hadamard condition - Hadamard factorisation theorem - Hamburger moment problem - Hard Lefschetz theorem - Hardy's inequality - Harmonic space - Harnack inequality - Hartogs theorem - Hausdorff moment problem - Hausdorff-Young theorem - Heinz inequality - Hermite-Weber function - Hessian of a vector field - Highest root - Hilbert algebra - Hilbert sum - Hirzebruch-Riemann-Roch formula - Hodge identities - Hodge metric - Hodge-Riemann bilinear relations - Holmgren method - Holmgren theorem - Holomorphic Euler characteristic - Holomorphic Lefschetz fixed point formula - Hopf formula - Hopf theorem - Hunt operator - Huyghens construction - Huyghens principle - Hypercohomology - Hyperelliptic surface - Hyperflex -

I

irregularities of distribution - Incidence correspondence - Incompressible mapping - Index of an operator - Interior function - Intermediate Jacobian - Invertible jet - Irregular linear system - Isochronous differential equation - Isotypic component - Iwasawa manifold - Iwasawa theorem -

J

Jacobi polynomial - Jacobi relation - Jacobs theorem - James embedding - Jensen formula - Jensen measure - Jessen-Wintner theorem - Jordan theorem (group theory) -

K

Dieter Kotschick - Kronecker Jugendtraum - kernel (integral equation) - Kac's theorem - Khinchin's inequality - Khinchin's theorem -Kneser-Glaeser theorem - Kirillov theorem - Kodaira classification of surfaces - Kodaira embedding theorem - Kodaira identity - Kodaira-Nakano vanishing theorem - Kolmogorov three series theorem - Kostant formula - Krein-Milman theorem - Kronecker integral - Krylov-Weinstein theorem - Kuga variety -

L

Lax pair - large sieve method - local cohomology - Lusztig - Lagrange-Duhamel method - Lax-Maslov operator - Lebesgue lemma - Lebesgue spine - Lefschetz class - Lefschetz decomposition - Lefschetz hyperplane theorem - Lefschetz pencil - Lelong number - Lelong theorem - Lepage decomposition - Leray-Hirsch theorem - Leray spectral sequence - Leray theorem - Levi extension theorem - Levi theorem - Levy inversion formula - Levy-Khinchin theorem - Lewy's example - Lichnerowicz lemma - Liouville field - Lie theorem - Lie transformation - Lie triple system - Line bundle associated to a divisor - Linked roots - Local duality theorem - Logmodular algebra - Lopatinski operator - Lüroth's theorem - Lusternik-Schnirelmann-Borsuk theorem - Lusternik-Schnirelmann category -

M

Müntz-Szasz theorem - monomial representation - Molien series - Manin-Mumford conjecture - Ludwig Maurer - microfunction - mixed Hodge structure - Mal'tsev theorem - Markov-Kakutani theorem - Mautner theorem - Max Noether's theorem - Mertens-Alexiewicz theorem - Meusnier theorem - Miniprincipal subgroup - Minkowski area - Minkowski formula - Mixing mapping - Mobius configuration - Monodromy principle - Monothetic group - Morse index - Morse inequality - Morton Brown's theorem - Mukhopadhyaya theorem - Multiplicity of a root - Muntz theorem -

N

Max Noether - Néron model -noncommutative harmonic analysis - Naimark theorem - Negative-definite function - Negative line bundle - Negative root - Nice subgroup - Noether formula - Noether theorem - Nondegenerate variety - Normal algebraic variety - Normal bundle - Normal coordinates - Normal projective connection - Nuclear operator -

O

Ore condition - obstruction theory - orthogonality relation - Oka's lemma - Oscillating integral

P

p-adic L-function - Puiseux expansion - prehomogeneous vector space - polarization of an algebraic form - principle of stationary phase - Pisot - Peterson inner product - Picard-Lefschetz formula - pinch point - p-adic solenoid - Palais theorem - Parabolic subalgebra - parametrix - Paratingent - Paul Cohen's theorem - Period matrix - Pham manifold - Phragmen-Brouwer theorem - Pieri formula - Pivotal root - Plancherel-Godement theorem - Plemelj formula - Plücker formula - Plücker relations - Plurisubharmonic function - Poincaré formula - Poincaré-Lelong equation - Poincaré line bundle - Poincaré recurrence theorem - Poincaré residue map - Poincaré series - Poincaré-Volterra theorem - Point-spectrum - Polar decomposition of an operator - Polarized abelian variety - Polycylinder - Porteous formula - Positive current - Primitive cycle - Primitive element (representation theory) - Primitive element (Hopf algebra) - Principal polarization - Principal symbol - Principle of domination - Prism lemma - Projective bundle - Projective connection - Projective structure - Prolongation of a differential system - propagation principle - proper mapping theorem - proper transform - Puiseux series - pure potential -

Q

quadratic differential - quasiperiodic - quasi-coherent sheaf - quadratic transformation - quadric line complex - quasi-ergodic set - quasi-invariant measure -

R

regular singularity - Ringed space - Walter Rudin - Hans Reiter - rational map - Riquier - C. P. Ramanujam - Rouse Ball chair - Rademacher function - Rademacher-Kolmogorov theorem - Rademacher-Menchov theorem - ramification divisor - rational normal curve - rational normal scroll - rational surface - Rauch comparison theorem - Reciprocal polars - Reciprocity laws - Reeb foliation - Reeb theorem - Regular integral element - Reiss relation - Rellich lemma - Rellich theorem - Resolvant family - Resultant - Riemann bilinear relations - Riemann conditions - Riemann-Hilbert problem - Riemann-Kempf singularity theorem - Riemann theorem - Riemann theta-divisor - F. and M. Riesz theorem - M. Riesz theorem - Rotational mean

S

Selmer group - Schubert calculus - Selmer group - Siegel modular form - scattering theory - Pierre Samuel - Stiefel - simple homotopy theory - Spencer cohomology - Shimura variety - Schubert calculus - Schubert symbol - Schur theorem - Schwarz procedure - Segal theorem - Siegel half-space - Sierpinski theorem - Singular element (Lie theory) - Sobolev lemma - Solenoidal group - Sonine formula - Special linear system - Spherical function - Splittable Lie algebra - Stationary trisecant - Steiner construction - Steiner-Minkowski formula - Steiner symmetrization - Stieltjes moment problem - Subimmersion - Superabundance - Symmetrized Lie algebra - Symmetric product of curves - Synge lemma - Synge theorem - Szegö-Kolmogorov-Krein theorem

T

Tate module - Tate-Shafarevich group - Tate-Néron height - Tate conjecture - Tannaka-Krein duality - Tannakian category - Tacnode - Tempered function - Theta-divisor - Thom transversality theorem - Titchmarsh-Kodaira formula - Todd polynomial - Torelli theorem - Transversal mappings - Trisecant - Twisted torus

U

unitary dilation- Umbilic - Universal Schubert coefficients

V

E. R. van Kampen - variation of Hodge structure - vanishing cycle - Vague topology - van der Corput theorem Very ample divisor - Virtual genus - Volterra operator - von Neumann ergodic theorem -

W

Joseph Wedderburn - Whitehead product - Wandering set - Wang sequence - Weakly reductive homogeneous space - Web - Weierstrass division theorem - Weierstrass point - Weil homomorphism - Weil reciprocity - Weitzenbock identity - Weyl basis - Weyl chamber - Weyl commutation relation - Weyl equidistribution theorem - Weyl formula - Weyl projective curvature - Weyl theorem - Whitney extension theorem - Whitney-Graustein theorem - Whitney product formula - Width of a set - Wiener-Kolmogorov theorem - Wiener-Levy theorem - Wiener tauberian theorem - Wirtinger inequality - Wirtinger theorem -

X

Y

] - yoga of weights (algebraic geometry) - Yano formula - Yoneda pairing -

Z

Zariski surface - Zariski's main theorem - Zariski's theorem on holomorphic functions - Zariski Riemann surface - Zariski space -Zaremba theorem - Zero-cycle - Zoll surface - Zonal spherical function -

Culled from list of mathematicians

Gibbsian ensemble - Hamilton-Jacobi theory - Hamming window - - Intersection theory - Last multiplier - method of exhaustion - Motivic Galois group - Nuclear space -Polygonal number theorem - Prime end - Ptolemy's theorem - Quasi-periodic function - Quasi-randomness - resolution of singularities - Scheduling theory - Six operations of Grothendieck - Topological tensor product - Zhukovsky-Kutta aerofoil - Asymptotic periods - Binary numeration - Cayley-Menger determinant - Coadjoint action - Coherence theorem - Cyclometric function - Dandelin-Gräffe method - Dependent type - Deterministic quantum mechanics - Hutton's formula - Impulsive coordinate - Integrable system - Lambert's projection - Lambert's trinomial equation - Large sieve method - Lyapunov methods - Menger-Urysohn dimension - Minkowski functional - Moment map - Moment space - Morley's problem - Normal derivative - Orlicz norm - Painlevé transcendents - Pappus chain - Pappus's harmonic theorem - Planetary theory - Plemelj-Sokhotsky equations - Poisson kernel - Poisson-Boltzmann equation - Prequantization - Riemann lemma - Rule of Succession - Sylvester's identity - Sylvester's sequence - Thom transversality theorem - Witt vector - Antifounded set theory - Arf invariant - Arf ring - Bombieri’s theorem - Borel space - Brauer lifting - Brauer's theorem on induced characters - Brauer-Siegel theorem - Calculus of two errors - Hasse-Arf theorem - Large sieve method - Liouville equation - Nonlinear wave - quasiconformal mapping - Grassmann-Cayley algebra - Cech homology - Schwarz-Christoffel transformation - Dandelin-Gräffe method

From list of number theory topics

Brauer-Siegel theorem - Higher reciprocity laws

Conjecture listings

Proved:

Thurston's conjecture on circle packings - Real Fatou conjecture - Vitushkin conjecture - Lichnerowicz conjecture - Bochner conjecture - Bloch's conjecture - Penrose conjecture - Calabi conjecture - Calabi-Yau conjectures - Milin conjecture - Robertson conjecture - Robbins conjecture - Fontaine-Mazur conjecture - Abhyankar's conjecture - Gray's conjecture -

• Ward's conjecture Theorem (Schmidt). Suppose is a non-degenerate linear recurrence sequence of order . Then N(U) << ...

Disproved:

Schoen-Yau conjecture

Open:

Smale's mean value conjecture - Schmidt conjecture- Shafarevich conjecture Stark conjecture Mumford-Shah conjecture Sendov conjecture spectral set conjecture Fatou conjecture Caratheodory conjecture Minimal volume gap conjecture Gromov-Lawson conjecture Strominger-Yau-Zaslow conjecture homological mirror conjecture Gopakumar-Vafa conjecture Virasoro conjecture Clemens conjecture Lovasz conjecture Minimal resolution conjecture Kocay reconstruction conjecture Finitistic gl dim conjecture Green's conjecture Abelian defect group conjecture Nakai's conjecture D'Oliveira's determinantal conjecture Deligne's conjecture Herzog-Schönheim conjecture Kaplansky's fifth conjecture Dade's conjecture BFSS conjecture Cherlin-Zilber conjecture Canonical element conjecture Alperin-McKay conjecture Jacquet's conjecture Friedland-Herminsky conjecture Sullivan's fixed point conjecture Nakayama's conjecture FGF-conjecture Berman conjecture

• Faith conjecture a right self-injective semiprimary ring is Quasi-Frobenuius

• Mishchenko-Fomenko conjecture

Bass conjecture Chinburg conjecture Connes-Kasparov conjecture Direct sum conjecture Fröberg conjecture Kontsevich's Hochschild cohomology conjecture Minkowski's conjecture Coates-Sinnott conjecture Equivariant Takagawa number conjecture Grothendieck-Katz p-curvature conjecture Anick's conjecture

• Rubin-Stark conjecture In the 1970s and early 1980s Stark developed a remarkable conjecture aimed at interpreting the first non-vanishing derivative of an Artin L-function L_{K/k, S}(s, \chi) at s=0 in terms of the arithmetic properties of the Galois extension of global fields K/k. Work of Tate, Chinburg, and Stark himself has revealed far reaching applications of Stark's Conjecture to Hilbert's 12-th Problem and the theory of Galois module structure of groups of units and ideal-class groups. In his search for new examples of Euler Systems,

Rubin has formulated in 1994 a strong version ("over Z", in Tate's terminology) of Stark's Conjecture for abelian L-functions of arbitrary order of vanishing at s=0. Our study of the functorial base-change behavior of Rubin's Conjecture led us to formulating a seemingly more natural Stark-type conjecture "over Z".

• Lange's conjecture If 0<s\le n'(n-n')(g-1), then there exist stable vector bundles with s_n'(E)=s. We prove this result for the generic curve.
• Connes-Kreimer conjecture
• Goncharov conjecture
• Bounded orbit conjecture
• Vojta's conjecture
• Bogomolov conjecture the commutator subgroup of the maximal quotient pro-l-group of the Galois group is free
• Hanna Neumann conjecture

If A and B are finitely generated non-trivial subgroups of a free group of finite rank, and I is the intersection of A and B, then rk(I)-1 <= (rk(A)-1)(rk(B)-1).

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Representation theory

Abel integral equation - Abel transformation - Acceptable Lie group - Accommodting orbit - Almost complex mapping - Analytic domination - Analytic mapping - Analytic vector - Banach representation - Bochner integral - Borel section - Boundary of a Lie group - Boundary subgroup - Bruhat lemma - c-function - Cartan integer - Cartan involution - Cartan subgroup - Casimir polynomial - Central character - Central eigendistribution - Chevalley's criterion - Chevalley's restriction theorem - Class one representation - Closure of an operator - Compactification of a Riemannian symmetric space - Complete set of representations - Completely invariant set - Complex distance - Complex semisimple group - Complexification of a reductive group - Connection index - Contragrediant representation - co-root - countable at infinity - Coxeter-Killing transformation - Cuspidal parabolic subgroup - Decent convergence - Differentiable representation - Differentiable vector - Adjoint of a differential operator - Discrete series - Discretely related groups - Dominant weight - Domination of parabolic pairs - Dual cone - Dual module - Dual space of a locally compact group - Eigendistribution - Elementary representation - Elliptic element - Exponents of a semisimple Lie algebra - Extended Burnside theorem - Finite reflection group - Fixed point property - Fundamental Cartan subalgebra - Fundamental system of roots - Fundamental theorem of invariant theory - Gangolli expansion - Garding subspace - Gelfand-Raikov theorem - Harmonic polynomial - Hermitian element - Highest exponent - Highest term - Highest weight - Hilbert bundle - Hilbert product - Hilbert representation - Holomorphic character - Horocycle - Horocyclic set of roots - Hull-kernel topology - Hyperbolic element - Index of a Weyl group element - Indivisible root - Mackey-Shoda criteria for induced representations - Inductive tensor product - Inductive topology - Inequalities of descent - Infinitesimal character - Infinitesimal equivalence - Infinitesimally unitary - Inhomogeneous Lorentz group - Integrable unitary representation - Intertwining form - Intertwining number theorem - Invariant integral - Irreducible root system - Isotypic submodule - Jacobson-Morosow threom - Kostant's character formula - Langlands decomposition - Large compact subgroup - Leading exponent - Leading term - Levi decomposition - Levi subalgebra - Levi subgroup - Lie's theorem - Liminaire - Mackey's imprimitivity theorem - Mackey's orbital analysis - Mackey's subgroup theorem - Maximal boundary - Minimal parabolic subgroup - Minimal regular norm - Multiplicity of a restricted root - Multiplier - Naimark equivalence - Nilpotent component - Non-reduced root system - Normal real form - Opposition involution - Paley-Weiner space - Parabolic rank - Parabolic set of roots - Parabolic subalgebra - Plancherel measure - Polar coordinate decomposition - Polynomial differential operator - Positive element - Positive system of roots - Postliminaire - Primitive invariant - Principal exponent - Principal part - Principal series - Projective tensor product - Projective topology - Quasi-invariant measure - Radial component of a differential operator - Ramification index - Rank of a connected Lie group - Rank of a Lie algebra - Rapidly decreasing function - Rational invariant - Rational representation - Reduced dual - Reducing series - Regular element - Regular left ideal - Regularization of an integral - Regularly related subgroups - Representation ring - Rho-function - Riemann-Roch theorem for Lie algebras - Root group - Satake diagram - Scattered subset - Schubert cell - Schur orthogonality relations - Schwartz's kernel theorem - Schwartz structure - Selberg principle - Semi-regular element - Singular element - Singular hyperplane - Skew differential operator - Skew element - Socle - Spherical Fourier transform - Spherical function - Spherical Gelfand transform - Spherical trace function - Split abelian subgroup - Split-rank - Standard Cartan subalgebra - Standard filtration - Standard parabolic subgroup - Standard representation - Standard semi-norm - Strict morphism - Strongly orthogonal system - Subquotient theorem - Symmetrization - Theorem of compacity - Tits system - Topological complete irreducibility - Topological irreducibility - Total degree - Transformation of descent - Transversal derivative - Transversality condition - Type I - Unipotent component - Unipotent element - - Unitary trick - Vector distribution - Wave packet - Weak containment - Weak differentiability - Weak inequality - Weak Selberg principle - Multiplicity of weight - Weight group - Weyl basis - Weyl chamber - Weyl's character formula - Weyl's dimension formula - Zonal spherical function - Trombi-Varadarajan theorem

Algebraic topology

Acyclic models theorem - Adams conjecture - Adams filtration - Adams spectral sequence - Additive cohomology operation - Admissible map - Admissible monomial - Admissible sequence - Alexander duality - Algebra over a coalgebra - Atiyah-Hirzebruch-Whitehead spectral sequence - Attaching a cell - Augmentation ideal - Boardman homomorphism - Bockstein homomorphism - Borel theorem - Cap-product - Cellular map - Chain homotopy - Characteristic map - Characteristic number - Chern character - Closure-finite - Clutching function - Coaction of H-cogroup - Cobordant - Coexact sequence of spaces - Cofibre sequence - Cohomology theory associated with a spectrum - Cotensor product - CW-substitute - Deformation retract - Degree of a map - Derived functor of inverse limit - Diagonal approximation - Divided polynomial algebra - edge homomorphism - Eilenberg complex - Eilenberg-MacLane spectrum - Eilenberg-Zilber theorem - e-invariant - Euler class - Exact homotopy sequence - Excisive triad - Extended comodule - Finite spectrum - Framed cobordism - Framing of a bundle - Free on models - Free resolution - Function of spectra - Gysin sequence - Hattori-Stong theorem - H-cogroup - H-group - Homology theory associated with a spectrum - Homotopy excision theorem - Homotopy suspension - Hopf isomorphism theorem - Indecomposable quotient - Integralilty preserving homomorphism - Iterated loop space - J-homomorphism - Layer filtration - Leray-Hirsch theorem - Leray-Serre spectral sequence - Loop space - Map of spectra - Microbundle - Mittag-Leffler condition - Newton polynomial - Normal bundle - Orientable fibration - Orientation class - Oriented cobordism - Pontryagin product - Pontryagin-Thom construction - Quaternionic projective space - Retract - Serre sequence - Simple system of generators - Skeletal filtration - Skeleton - Slant product - Smash product of spectra - Space of paths - Spherical fibration - Spin cobordism - Stable cohomology operation - Stable homotopy group - Stable stem - Steenrod algebra - Steenrod square - Strong deformation retract - Subspectrum - Symplectic cobordism - Thom spectrum - Transgression - Transverse regular - Tubular neighborhood - Unitary cobordism - Universal element - Unoriented cobordism - Wang sequence - Weak H-group - Weak H-group - Zeeman's comparison theorem