Infinitesimal K-theory

Details Infinitesimal K-theory Infinitesimal K-theory

2000-01-25

arxiv.org/abs/math/0001138v1

J. Reine Angew. Math. 503 (1998), 129-160

Mathematics

K-Theory and Homology

31 pages, uses xy macros

Scientific paper

In this paper we study the fiber F of the rational Jones-Goodwillie character $$ F:=\hofiber(ch:K^\rat(A)@>>>HN^\rat(A)) $$ going from K-theory to negative cyclic homology of associative rings. We describe this fiber F in terms of sheaf cohomology. We prove that, for $n\ge 1$, there is an isomorphism: $$ \pi_n(F)\cong H^{-n}_{inf}(A,K^\rat) $$ between the homotopy of the fiber and the hypercohomology groups of $K^\rat$ on a non-commutative version of Grothendieck's infinitesimal site.

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