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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****►****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**►****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****►****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****►****14-00 General reference works (handbooks, dictionaries, bibliographies, etc.)****►****14Axx Foundations****►****14Bxx Local theory****►****14Cxx Cycles and subschemes****►****14Dxx Families, fibrations****►****14Exx Birational geometry****►****14Fxx (Co)homology theory****▼****14Gxx Arithmetic problems. Diophantine geometry**- 14G05 Rational points
- 14G10 Zeta-functions and related questions
- 14G15 Finite ground fields
- 14G20 Local ground fields
- 14G22 Rigid analytic geometry
- 14G25 Global ground fields
- 14G27 Other nonalgebraically closed ground fields
- 14G32 Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory)
- 14G35 Modular and Shimura varieties
- 14G40 Arithmetic varieties and schemes; Arakelov theory; heights
- 14G50 Applications to coding theory and cryptography
- 14G99 None of the above, but in this section

**►****14Hxx Curves****▼****14Jxx Surfaces and higher-dimensional varieties**- 14J10 Families, moduli, classification: algebraic theory
- 14J15 Moduli, classification: analytic theory; relations with modular forms
- 14J17 Singularities
- 14J20 Arithmetic ground fields
- 14J25 Special surfaces
- 14J26 Rational and ruled surfaces
- 14J27 Elliptic surfaces
- 14J28
*K3*surfaces and Enriques surfaces - 14J29 Surfaces of general type
- 14J30
*3*-folds - 14J32 Calabi-Yau manifolds, mirror symmetry
- 14J35
*4*-folds - 14J40
*n*-folds (*n > 4*) - 14J45 Fano varieties
- 14J50 Automorphisms of surfaces and higher-dimensional varieties
- 14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
- 14J70 Hypersurfaces
- 14J80 Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants)
- 14J81 Relationships with physics
- 14J99 None of the above, but in this section

**►****14Kxx Abelian varieties and schemes****►****14Lxx Algebraic groups****►****14Mxx Special varieties****►****14Nxx Projective and enumerative geometry****►****14Pxx Real algebraic and real analytic geometry****►****14Qxx Computational aspects in algebraic geometry****►****14Rxx Affine 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**- 18A05 Definitions, generalizations
- 18A10 Graphs, diagram schemes, precategories
- 18A15 Foundations, relations to logic and deductive systems
- 18A20 Epimorphisms, monomorphisms, special classes of morphisms, null morphisms
- 18A22 Special properties of functors (faithful, full, etc.)
- 18A23 Natural morphisms, dinatural morphisms
- 18A25 Functor categories, comma categories
- 18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)
- 18A32 Factorization of morphisms, substructures, quotient structures, congruences, amalgams
- 18A35 Categories admitting limits (complete categories), functors preserving limits, completions
- 18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)
- 18A99 None of the above, but in this section

**▼****18Bxx Special categories**- 18B05 Category of sets, characterizations
- 18B10 Category of relations, additive relations
- 18B15 Embedding theorems, universal categories
- 18B20 Categories of machines, automata, operative categories
- 18B25 Topoi
- 18B30 Categories of topological spaces and continuous mappings
- 18B35 Preorders, orders and lattices (viewed as categories)
- 18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories)
- 18B99 None of the above, but in this section

**►****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**

**▼****19-XX***K*-theory**►****19-00 General reference works (handbooks, dictionaries, bibliographies, etc.)****►****19Axx Grothendieck groups and***K*_{0}**▼****19Bxx Whitehead groups and***K*_{1}**►****19Cxx Steinberg groups and***K*_{2}**►****19Dxx Higher algebraic***K*-theory**▼****19Exx***K*-theory in geometry**►****19Fxx***K*-theory in number theory**►****19Gxx***K*-theory of forms**►****19Jxx Obstructions from topology****►****19Kxx***K*-theory and operator algebras**►****19Lxx Topological***K*-theory- 19M05 Miscellaneous applications of
*K*-theory

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

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

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