11Fxx Discontinuous groups and automorphic forms [See also 11R39, 11S37, 14Gxx, 14Kxx, 22E50, 22E55, 30F35, 32Nxx] {For relations with quadratic forms, see 11E45} 18868
11G40 \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture [See also 14G10] 1276
14-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to algebraic geometry 26
14-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry 476
14-03 History of algebraic geometry [Consider also classification numbers pertaining to Section 01-XX] 699
14A30 Fundamental constructions in algebraic geometry involving higher and derived categories (homotopical algebraic geometry, derived algebraic geometry, etc.) {For categorical aspects, see 18Fxx, 18Gxx} 27
14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry [See also 13H15] 1409
14C30 Transcendental methods, Hodge theory (algebro-geometric aspects) [See also 14D07, 32G20, 32J25, 32S35], Hodge conjecture 1786
14D20 Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13} 2482
14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) [See also 32L25, 81Txx] 1458
14E15 Global theory and resolution of singularities (algebro-geometric aspects) [See also 14B05, 32S20, 32S45] 1608
14F08 Derived categories of sheaves, dg categories, and related constructions in algebraic geometry [See also 14A30, 14F06, 18Gxx] 271
14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials [See also 13Nxx, 32C38] 1340
14F43 Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) 754
14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) [See also 11G40] 1559
14G32 Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory) 298
14G50 Applications to coding theory and cryptography of arithmetic geometry [See also 94A60, 94B27, 94B40] 1779
14J17 Singularities of surfaces or higher-dimensional varieties [See also 14B05, 14E15, 32S05, 32S25] 1987
14J20 Arithmetic ground fields for surfaces or higher-dimensional varieties [See also 11Dxx, 11G25, 11G35, 14Gxx] 378
14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli [See also 14D20, 14F06, 14H60, 32Lxx] 1778
14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) [See also 13F15, 13F45, 13H10] 1271
14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) [See also 53D45] 1833
14Qxx Computational aspects in algebraic geometry {For software etc., see 14-04} [See also 12-08, 13Pxx, 68W30] 2616
14Q25 Computational algebraic geometry over arithmetic ground fields [See also 14Gxx, 14H25, 14Kxx] 1
14T10 Foundations of tropical geometry and relations with algebra {For algebraic aspects, see 15A80} 37
18-XX Category theory; homological algebra {For commutative rings, see 13Dxx; for associative rings, see 16Exx; for groups, see 20Jxx; for topological groups and related structures, see 57Txx; for algebraic topology, see also 55Nxx, 55Uxx} 29175
18F20 Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) [See also 14F06, 14F08, 32C35, 32L10, 54B40, 55N30] 1173
18F25 Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects) [See also 11Exx, 11R70, 11S70, 12-XX, 13D15, 14Cxx, 16E20, 19-XX, 46L80, 57R65, 57R67] 1816
19E15 Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects) [See also 14C25, 14C35, 14F42] 484
32-XX Several complex variables and analytic spaces {For infinite-dimensional holomorphy, see also 46G20, 58B12} 47801
32B25 Triangulation and topological properties of semi-analytic andsubanalytic sets, and related questions 85
32Jxx Compact analytic spaces {For Riemann surfaces, see 14Hxx, 30Fxx; for algebraic theory, see 14Jxx} 2709
34C08 Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) 377
35Qxx Partial differential equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05] 115329
35Q76 Einstein equations {For several complex variables and analytic spaces, see 32Q40; for differential geometry, see 53C07; for relativity and gravitational theory, see 83C05, 83C25, 83D05} 229
37-XX Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] 120321
37Jxx Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems [See also 53Dxx, 70Fxx, 70Hxx] 18302
37J38 Relations of finite-dimensional Hamiltonian and Lagrangian systems with algebraic geometry, complex analysis, special functions 22
37J39 Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) [See also 53D20] 125
37Kxx Dynamical system aspects of infinite-dimensional Hamiltonian and Lagrangian systems [See also 35Axx, 35Qxx] 18801
37K20 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions [See also 14H70] 883
37K25 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry 699
46-XX Functional analysis {For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx} 128356
46Cxx Inner product spaces and their generalizations, Hilbert spaces {For function spaces, see 46Exx} 5055
46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) 1903
46Lxx Selfadjoint operator algebras (\(C^*\)-algebras, von Neumann (\(W^*\)-) algebras, etc.) [See also 22D25, 47Lxx] 24908
51-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to geometry 44
51F15 Reflection groups, reflection geometries [See also 20H10, 20H15] {For Coxeter groups, see 20F55} 1142
51M16 Inequalities and extremum problems in real or complex geometry {For convex problems, see 52A40} 899
51M35 Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations) [See also 14M15] 339
51Pxx Classical or axiomatic geometry and physics (should also be assigned at least one other classification number from Sections 70-XX–86-XX) 350
51P05 Classical or axiomatic geometry and physics (should also be assigned at least one other classification number from Sections 70-XX–86-XX) 341
52-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to convex and discrete geometry 12
52-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to convex and discrete geometry 225
52-02 Research exposition (monographs, survey articles) pertaining to convex and discrete geometry 433
52-03 History of convex and discrete geometry [Consider also classification numbers pertaining to Section 01-XX] 117
52A21 Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry) [See also 46Bxx] 705
52A22 Random convex sets and integral geometry (aspects of convex geometry) [See also 53C65, 60D05] 1353
52A38 Length, area, volume and convex sets (aspects of convex geometry) [See also 26B15, 28A75, 49Q20] 1067
52B05 Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) [See also 05Cxx] 1440
52B20 Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) [See also 06A11, 13F20, 13F55, 13Hxx, 52C05, 52C07] 1249
52B40 Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) [See also 05B35, 52Cxx] 703
52B55 Computational aspects related to convexity {For computational methods, see 52-08; for computational geometry and algorithms, see 68Q25, 68U05; for numerical algorithms, see 65Yxx} [See also 68Uxx] 1319
52C05 Lattices and convex bodies in \(2\) dimensions (aspects of discrete geometry) [See also 11H06, 11H31, 11P21] 342
52C07 Lattices and convex bodies in \(n\) dimensions (aspects of discrete geometry) [See also 11H06, 11H31, 11P21] 1035
52C15 Packing and covering in \(2\) dimensions (aspects of discrete geometry) [See also 05B40, 11H31] 947
52C17 Packing and covering in \(n\) dimensions (aspects of discrete geometry) [See also 05B40, 11H31] 2406
52C35 Arrangements of points, flats, hyperplanes (aspects of discrete geometry) [See also 14N20, 32S22] 1337
53-XX Differential geometry {For differential topology, see 57Rxx; for foundational questions of differentiable manifolds, see 58Axx} 123719
53-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to differential geometry 36
53-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to differential geometry 1044
53-03 History of differential geometry [Consider also classification numbers pertaining to Section 01-XX] 550
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42] 4977
53Cxx Global differential geometry [See also 51H25, 58-XX] {For related bundle theory, see 55Rxx, 57Rxx} 72866
53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) [See also 32Q20] 1898
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) 8900
53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60] 4683
53C23 Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces 1798
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42] 7275
53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics) [See also 58B20] 2764
53C65 Integral geometry [See also 52A22, 60D05]; differential forms, currents, etc. [See mainly 58Axx] 2341
53D37 Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category [See also 14J33] 360
57Rxx Differential topology {For foundational questions of differentiable manifolds, see 58Axx; for infinite-dimensional manifolds, see 58Bxx} 20809
58-XX Global analysis, analysis on manifolds [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx] {For geometric integration theory, see 49Q15} 65551
58Jxx Partial differential equations on manifolds; differential operators [See also 32Wxx, 35-XX, 53Cxx] 24381
60-XX Probability theory and stochastic processes {For additional applications, see 05Cxx, 11Kxx, 34-XX, 35-XX, 62-XX, 90-XX, 76-XX, 81-XX, 82-XX, 91-XX, 92-XX, 93-XX, 94-XX} 214299
65Dxx Numerical approximation and computational geometry (primarily algorithms) {For theoretical aspects, see 41-XX, 68Uxx} 35995
65D18 Numerical aspects of computer graphics, image analysis, and computational geometry [See also 51N05, 68U05] 4958
68-XX Computer science {For papers containing software, source code, etc. in a specific mathematical area, see the classification number -04 in that area} 367922
68U05 Computer graphics; computational geometry (digital and algorithmic aspects) {For methods of numerical mathematics, see 65D18} 14774
70-XX Mechanics of particles and systems {For relativistic mechanics, see 83A05, 83C10; for statistical mechanics, see 82-XX} 66342
81Q30 Feynman integrals and graphs; applications of algebraic topology and algebraic geometry [See also 14D05, 32S40] 1049
94B27 Geometric methods (including applications of algebraic geometry) applied to coding theory [See also 11T71, 14G50] 1466
94B75 Applications of the theory of convex sets and geometry of numbers (covering radius, etc.) to coding theory [See also 11H31, 11H71] 435