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**►****Foundations****▼****Algebra****▼****11-XX Number theory****►****11-00 General reference works (handbooks, dictionaries, bibliographies, etc.)****►****11Axx Elementary number theory****►****11Bxx Sequences and sets****►****11Cxx Polynomials and matrices****►****11Dxx Diophantine equations****▼****11Exx Forms and linear algebraic groups**- 11E04 Quadratic forms over general fields
- 11E08 Quadratic forms over local rings and fields
- 11E10 Forms over real fields
- 11E12 Quadratic forms over global rings and fields
- 11E16 General binary quadratic forms
- 11E20 General ternary and quaternary quadratic forms; forms of more than two variables
- 11E25 Sums of squares and representations by other particular quadratic forms
- 11E39 Bilinear and Hermitian forms
- 11E41 Class numbers of quadratic and Hermitian forms
- 11E45 Analytic theory (Epstein zeta functions; relations with automorphic forms and functions)
- 11E57 Classical groups
- 11E70
*K*-theory of quadratic and Hermitian forms - 11E72 Galois cohomology of linear algebraic groups
- 11E76 Forms of degree higher than two
- 11E81 Algebraic theory of quadratic forms; Witt groups and rings
- 11E88 Quadratic spaces; Clifford algebras
- 11E95
*p*-adic theory - 11E99 None of the above, but in this section

**▼****11Fxx Discontinuous groups and automorphic forms**- 11F03 Modular and automorphic functions
- 11F06 Structure of modular groups and generalizations; arithmetic groups
- 11F11 Modular forms, one variable
- 11F12 Automorphic forms, one variable
- 11F20 Dedekind eta function, Dedekind sums
- 11F22 Relationship to Lie algebras and finite simple groups
- 11F23 Relations with algebraic geometry and topology
- 11F25 Hecke-Petersson operators, differential operators (one variable)
- 11F27 Theta series; Weil representation
- 11F30 Fourier coefficients of automorphic forms
- 11F32 Modular correspondences, etc.
- 11F33 Congruences for modular and
*p*-adic modular forms - 11F37 Forms of half-integer weight; nonholomorphic modular forms
- 11F41 Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces
- 11F46 Siegel modular groups and their modular and automorphic forms
- 11F50 Jacobi forms
- 11F55 Other groups and their modular and automorphic forms (several variables)
- 11F60 Hecke-Petersson operators, differential operators (several variables)
- 11F66 Dirichlet series and functional equations in connection with modular forms
- 11F67 Special values of automorphic
*L*-series, periods of modular forms, cohomology, modular symbols - 11F70 Representation-theoretic methods; automorphic representations over local and global fields
- 11F72 Spectral theory; Selberg trace formula
- 11F75 Cohomology of arithmetic groups
- 11F80 Galois representations
- 11F85
*p*-adic theory, local fields - 11F99 None of the above, but in this section

**►****11Gxx Arithmetic algebraic geometry (Diophantine geometry)****►****11Hxx Geometry of numbers****►****11Jxx Diophantine approximation, transcendental number theory****▼****11Kxx Probabilistic theory: distribution modulo***1*; metric theory of algorithms- 11K06 General theory of distribution modulo
*1* - 11K16 Normal numbers, radix expansions, etc.
- 11K31 Special sequences
- 11K36 Well-distributed sequences and other variations
- 11K38 Irregularities of distribution, discrepancy
- 11K41 Continuous,
*p*-adic and abstract analogues - 11K45 Pseudo-random numbers; Monte Carlo methods
- 11K50 Metric theory of continued fractions
- 11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension
- 11K60 Diophantine approximation
- 11K65 Arithmetic functions
- 11K70 Harmonic analysis and almost periodicity
- 11K99 None of the above, but in this section

- 11K06 General theory of distribution modulo
**►****11Lxx Exponential sums and character sums****►****11Mxx Zeta and***L*-functions: analytic theory**►****11Nxx Multiplicative number theory****►****11Pxx Additive number theory; partitions****▼****11Rxx Algebraic number theory: global fields**- 11R04 Algebraic numbers; rings of algebraic integers
- 11R06 PV-numbers and generalizations; other special algebraic numbers
- 11R09 Polynomials (irreducibility, etc.)
- 11R11 Quadratic extensions
- 11R16 Cubic and quartic extensions
- 11R18 Cyclotomic extensions
- 11R20 Other abelian and metabelian extensions
- 11R21 Other number fields
- 11R23 Iwasawa theory
- 11R27 Units and factorization
- 11R29 Class numbers, class groups, discriminants
- 11R32 Galois theory
- 11R33 Integral representations related to algebraic numbers; Galois module structure of rings of integers
- 11R34 Galois cohomology
- 11R37 Class field theory
- 11R39 Langlands-Weil conjectures, nonabelian class field theory
- 11R42 Zeta functions and
*L*-functions of number fields - 11R44 Distribution of prime ideals
- 11R45 Density theorems
- 11R47 Other analytic theory
- 11R52 Quaternion and other division algebras: arithmetic, zeta functions
- 11R54 Other algebras and orders, and their zeta and
*L*-functions - 11R56 Adčle rings and groups
- 11R58 Arithmetic theory of algebraic function fields
- 11R60 Cyclotomic function fields (class groups, Bernoulli objects, etc.)
- 11R65 Class groups and Picard groups of orders
- 11R70
*K*-theory of global fields - 11R80 Totally real and totally positive fields
- 11R99 None of the above, but in this section

**►****11Sxx Algebraic number theory: local and***p*-adic fields**►****11Txx Finite fields and commutative rings (number-theoretic aspects)****►****11Uxx Connections with logic****►****11Yxx Computational number theory**- 11Zxx Miscellaneous applications of number theory

**▼****12-XX Field theory and polynomials****►****12-00 General reference works (handbooks, dictionaries, bibliographies, etc.)****▼****12Dxx Real and complex fields****▼****12Exx General field theory****►****12Fxx Field extensions****▼****12Gxx Homological methods (field theory)****▼****12Hxx Differential and difference algebra****▼****12Jxx Topological fields****►****12Kxx Generalizations of fields****►****12Lxx Connections with logic**- 12Y05 Computational aspects of field theory and polynomials

**►****13-XX Commutative rings and algebras****►****14-XX Algebraic geometry****►****15-XX Linear and multilinear algebra; matrix theory****►****16-XX Associative rings and algebras****►****17-XX Nonassociative rings and algebras****▼****18-XX Category theory; homological algebra****►****18-00 General reference works (handbooks, dictionaries, bibliographies, etc.)****►****18Axx General theory of categories and functors****►****18Bxx Special categories****►****18Cxx Categories and theories****▼****18Dxx Categories with structure**- 18D05 Double categories,
*2*-categories, bicategories and generalizations - 18D10 Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories
- 18D15 Closed categories (closed monoidal and Cartesian closed categories, etc.)
- 18D20 Enriched categories (over closed or monoidal categories)
- 18D25 Strong functors, strong adjunctions
- 18D30 Fibered categories
- 18D35 Structured objects in a category (group objects, etc.)
- 18D50 Operads
- 18D99 None of the above, but in this section

- 18D05 Double categories,
**►****18Exx Abelian categories****►****18Fxx Categories and geometry****▼****18Gxx Homological algebra**- 18G05 Projectives and injectives
- 18G10 Resolutions; derived functors
- 18G15 Ext and Tor, generalizations, Künneth formula
- 18G20 Homological dimension
- 18G25 Relative homological algebra, projective classes
- 18G30 Simplicial sets, simplicial objects (in a category)
- 18G35 Chain complexes
- 18G40 Spectral sequences, hypercohomology
- 18G50 Nonabelian homological algebra
- 18G55 Homotopical algebra
- 18G60 Other (co)homology theories
- 18G99 None of the above, but in this section

**►****19-XX***K*-theory**►****20-XX Group theory and generalizations**

**►****Analysis****►****Differential Equations****►****Transformations****▼****Geometry****►****Statistics****►****Applied Mathematics****►****Didactics**

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