Stable \(K\)-theory of finite fields. (English) Zbl 0929.19002

Betley, Stanislaw

\(K\)-Theory 17, No. 2, 103-111 (1999).

Let \(R\) be a finite field. It is shown that the stable \(K\)-theory of \(R\) with bifunctor coefficients of finite degree is equal to the topological Hochschild homology of \(R\) with the same coefficients. There is a similar result for cohomology. For general rings, but only for bilinear bifunctors, this result was given by B. I. Dundas and R. McCarthy [“Stable \(K\)-theory and topological Hochschild homology”, Ann. Math., II. Ser. 140, No. 3, 685-701 (1994; Zbl 0833.55007), and Erratum, ibid. 142, No. 2, 425-426 (1995; Zbl 0839.55003)].

Reviewer: R.J.Steiner (Glasgow)

MSC:

19D55	\(K\)-theory and homology; cyclic homology and cohomology
16E40	(Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.)
18E25	Derived functors and satellites (MSC2010)
18G10	Resolutions; derived functors (category-theoretic aspects)
11T99	Finite fields and commutative rings (number-theoretic aspects)

Keywords:

stable \(K\)-theory; topological Hochschild homology

Citations:

Zbl 0833.55007; Zbl 0839.55003