Classification Search Result

Mathematics Subject Classification – MSC2020

19-XX

\(K\)-theory [See also 16E20, 18F25]

9475

19-00

General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to \(K\)-theory

19-01

Introductory exposition (textbooks, tutorial papers, etc.) pertaining to \(K\)-theory

19-02

Research exposition (monographs, survey articles) pertaining to \(K\)-theory

132

19-03

History of \(K\)-theory [Consider also classification numbers from Section 01-XX]

19-04

Software, source code, etc. for problems pertaining to \(K\)-theory

19-06

Proceedings, conferences, collections, etc. pertaining to \(K\)-theory

19-08

Computational methods for problems pertaining to \(K\)-theory

19-11

Research data for problems pertaining to \(K\)-theory

19Axx

Grothendieck groups and \(K_0\) [See also 13D15, 18F30]

1243

19A13

Stability for projective modules [See also 13C10]

140

19A15

Efficient generation of modules

19A22

Frobenius induction, Burnside and representation rings

637

19A31

\(K_0\) of group rings and orders

187

19A49

\(K_0\) of other rings

179

19A99

None of the above, but in this section

19Bxx

Whitehead groups and \(K_1\)

696

19B10

Stable range conditions

243

19B14

Stability for linear groups

141

19B28

\(K_1\) of group rings and orders [See also 57Q10]

179

19B37

Congruence subgroup problems [See also 20H05]

19B99

None of the above, but in this section

121

19Cxx

Steinberg groups and \(K_2\)

496

19C09

Central extensions and Schur multipliers

190

19C20

Symbols, presentations and stability of \(K_2\)

131

19C30

\(K_2\) and the Brauer group

19C40

Excision for \(K_2\)

19C99

None of the above, but in this section

103

19Dxx

Higher algebraic \(K\)-theory

2421

19D06

\(Q\)- and plus-constructions

106

19D10

Algebraic \(K\)-theory of spaces

240

19D23

Symmetric monoidal categories [See also 18M05]

206

19D25

Karoubi-Villamayor-Gersten \(K\)-theory

19D35

Negative \(K\)-theory, NK and Nil

168

19D45

Higher symbols, Milnor \(K\)-theory

358

19D50

Computations of higher \(K\)-theory of rings [See also 13D15, 16E20]

292

19D55

\(K\)-theory and homology; cyclic homology and cohomology [See also 18G90]

1064

19D99

None of the above, but in this section

171

19Exx

\(K\)-theory in geometry

1293

19E08

\(K\)-theory of schemes [See also 14C35]

428

19E15

Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects) [See also 14C25, 14C35, 14F42]

647

19E20

Relations of \(K\)-theory with cohomology theories [See also 14Fxx]

233

19E99

None of the above, but in this section

19Fxx

\(K\)-theory in number theory [See also 11R70, 11S70]

868

19F05

Generalized class field theory (\(K\)-theoretic aspects) [See also 11G45]

115

19F15

Symbols and arithmetic (\(K\)-theoretic aspects) [See also 11R37]

207

19F27

Étale cohomology, higher regulators, zeta and \(L\)-functions (\(K\)-theoretic aspects) [See also 11G40, 11R42, 11S40, 14F20, 14G10]

470

19F99

None of the above, but in this section

19Gxx

\(K\)-theory of forms [See also 11Exx]

476

19G05

Stability for quadratic modules

19G12

Witt groups of rings [See also 11E81]

197

19G24

\(L\)-theory of group rings [See also 11E81]

100

19G38

Hermitian \(K\)-theory, relations with \(K\)-theory of rings

155

19G99

None of the above, but in this section

19Jxx

Obstructions from topology

229

19J05

Finiteness and other obstructions in \(K_0\)

19J10

Whitehead (and related) torsion

19J25

Surgery obstructions (\(K\)-theoretic aspects) [See also 57R67]

117

19J35

Obstructions to group actions (\(K\)-theoretic aspects)

19J99

None of the above, but in this section

19Kxx

\(K\)-theory and operator algebras [See mainly 46L80, and also 46M20]

1855

19K14

\(K_0\) as an ordered group, traces

212

19K33

Ext and \(K\)-homology [See also 55N22]

191

19K35

Kasparov theory (\(KK\)-theory) [See also 58J22]

660

19K56

Index theory [See also 58J20, 58J22]

817

19K99

None of the above, but in this section

177

19Lxx

Topological \(K\)-theory [See also 55N15, 55R50, 55S25]

1228

19L10

Riemann-Roch theorems, Chern characters

207

19L20

\(J\)-homomorphism, Adams operations [See also 55Q50]

19L41

Connective \(K\)-theory, cobordism [See also 55N22]

123

19L47

Equivariant \(K\)-theory [See also 55N91, 55P91, 55Q91, 55R91, 55S91]

516

19L50

Twisted \(K\)-theory; differential \(K\)-theory

174

19L64

Geometric applications of topological \(K\)-theory

145

19L99

None of the above, but in this section

102

19Mxx

Miscellaneous applications of \(K\)-theory

121

19M05

Miscellaneous applications of \(K\)-theory

120

19M99

None of the above, but in this section

Overview

General and overarching topics; collections

History and biography

Mathematical logic and foundations

Combinatorics

Order, lattices, ordered algebraic structures

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\(K\)-theory

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Approximations and expansions

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Examples

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Mathematics Subject Classification – MSC2020

Overview