| 19-XX | | Prev: 18 | Up: Top | Next: 20 | |
| $K$-theory [xref: 18F25] | |
| [See also 16E20, 18F25] |
19-00|
General reference works (handbooks, dictionaries, bibliographies, etc.)
| 19-01 |
Instructional exposition (textbooks, tutorial papers, etc.)
| 19-02 |
Research exposition (monographs, survey articles)
| 19-03 |
Historical (must also be assigned at least one classification number from Section 01)
| 19-04 |
Explicit machine computation and programs (not the theory of computation or programming)
| 19-06 |
Proceedings, conferences, collections, etc.
| |
19Axx
| Grothendieck groups and $K_0$ [See also 13D15, 18F30]
[xref: 13D15, 16E20, 18F30]
| 19A13 |
Stability for projective modules [See also 13C10]
[xref: 13C10, 16D40]
| 19A15 |
Efficient generation
| 19A22 |
Frobenius induction, Burnside and representation rings
[xref: 20Cxx]
| 19A31 |
$K_0$ of group rings and orders
[xref: 11R34]
| 19A49 |
$K_0$ of other rings
| 19A99 |
None of the above, but in this section
| |
19Bxx
| Whitehead groups and $K_1$
| 19B10 |
Stable range conditions
| 19B14 |
Stability for linear groups
| 19B28 |
$K_1$ of group rings and orders [See also 57Q10]
[xref: 57Q10]
| 19B37 |
Congruence subgroup problems [See also 20H05]
[xref: 20H05]
| 19B99 |
None of the above, but in this section
| |
19Cxx
| Steinberg groups and $K_2$
| 19C09 |
Central extensions and Schur multipliers
| 19C20 |
Symbols, presentations and stability of $K_2$
| 19C30 |
$K_2$ and the Brauer group
| 19C40 |
Excision for $K_2$
| 19C99 |
None of the above, but in this section
| |
19Dxx
| Higher algebraic $K$-theory
| 19D06 |
$Q$- and plus-constructions
| 19D10 |
Algebraic $K$-theory of spaces
| 19D23 |
Symmetric monoidal categories [See also 18D10]
[xref: 18D10]
| 19D25 |
Karoubi-Villamayor-Gersten $K$-theory
| 19D35 |
Negative $K$-theory, NK and Nil
| 19D45 |
Higher symbols, Milnor $K$-theory
| 19D50 |
Computations of higher $K$-theory of rings [See also 13D15, 16E20]
[xref: 13D15, 16E20]
| 19D55 |
$K$-theory and homology; cyclic homology and cohomology [See also 18G60]
[xref: 18G60, 55S25]
| 19D99 |
None of the above, but in this section
| |
19Exx
| $K$-theory in geometry
[xref: 14C35]
| 19E08 |
$K$-theory of schemes [See also 14C35]
| 19E15 |
Algebraic cycles and motivic cohomology [See also 14C25, 14C35]
| 19E20 |
Relations with cohomology theories [See also 14Fxx]
[xref: 14C40]
| 19E99 |
None of the above, but in this section
| |
19Fxx
| $K$-theory in number theory [See also 11R70, 11S70]
[xref: 11R70, 11S70]
| 19F05 |
Generalized class field theory [See also 11G45]
[xref: 11G45]
| 19F15 |
Symbols and arithmetic [See also 11R37]
| 19F27 |
Étale cohomology, higher regulators, zeta and $L$-functions [See also 11G40, 11R42, 11S40, 14F20, 14G10]
[xref: 11R42, 11S40]
| 19F99 |
None of the above, but in this section
| |
19Gxx
| $K$-theory of forms [See also 11Exx]
[xref: 11Exx]
| 19G05 |
Stability for quadratic modules
| 19G12 |
Witt groups of rings [See also 11E81]
[xref: 11E81]
| 19G24 |
$L$-theory of group rings [See also 11E81]
[xref: 11E81]
| 19G38 |
Hermitian $K$-theory, relations with $K$-theory of rings
| 19G99 |
None of the above, but in this section
| |
19Jxx
| Obstructions from topology
| 19J05 |
Finiteness and other obstructions in $K_0$
| 19J10 |
Whitehead (and related) torsion
| 19J25 |
Surgery obstructions [See also 57R67]
[xref: 57R67]
| 19J35 |
Obstructions to group actions
| 19J99 |
None of the above, but in this section
| |
19Kxx
| $K$-theory and operator algebras [See mainly 46L80, and also 46M20]
[xref: 46L80, 46M20]
| 19K14 |
$K_0$ as an ordered group, traces
| 19K33 |
EXT and $K$-homology [See also 55N22]
| 19K35 |
Kasparov theory ($KK$-theory) [See also 58J22]
| 19K56 |
Index theory [See also 58J20, 58J22]
[xref: 58J20, 58J22]
| 19K99 |
None of the above, but in this section
| |
19Lxx
| Topological $K$-theory [See also 55N15, 55R50, 55S25]
[xref: 55N15, 55R50, 55S25]
| 19L10 |
Riemann-Roch theorems, Chern characters
[xref: 14C40]
| 19L20 |
$J$-homomorphism, Adams operations [See also 55Q50]
[xref: 55Q50]
| 19L41 |
Connective $K$-theory, cobordism [See also 55N22]
[xref: 55N22]
| 19L47 |
Equivariant $K$-theory [See also 55N91, 55P91, 55Q91, 55R91, 55S91]
[xref: 55N91, 55P91, 55Q91, 55R91, 55S91]
| 19L64 |
Computations, geometric applications
| 19L99 |
None of the above, but in this section
| |
19M05
| Miscellaneous applications of $K$-theory
| |