Infinitesimal K-theory
Guillermo Cortiñas
Abstract
In this paper we study the fiber F of the rational Jones-Goodwillie character F:=(ch:K(A)@>>>HN(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 1, there is an isomorphism: πn(F) H-ninf(A,K) between the homotopy of the fiber and the hypercohomology groups of K on a non-commutative version of Grothendieck's infinitesimal site.
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