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

##### 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
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