Chern classes in algebraic K-theory. (English) Zbl 0541.18008

Shekhtman, V. V.

Trans. Mosc. Math. Soc. 1984, No. 1, 243-271 (1984).

Translation from Tr. Mosk. Mat. O.-va 45, 237-264 (Russian) (1982; Zbl 0515.18008).

MSC:

18F25	Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects)
14C35	Applications of methods of algebraic \(K\)-theory in algebraic geometry
57R20	Characteristic classes and numbers in differential topology
11R37	Class field theory
14F20	Étale and other Grothendieck topologies and (co)homologies
14F40	de Rham cohomology and algebraic geometry
11S70	\(K\)-theory of local fields
14L30	Group actions on varieties or schemes (quotients)
11R70	\(K\)-theory of global fields

Keywords:

Chern classes; de Rham cohomology; Grothendieck K-functor; singular cohomology; étale cohomology; Galois symbol of Tate; n-dimensional class field theory; Hodge cohomology; crystalline cohomology