Infinitesimal K-theory, by Guillermo Cortiñas

In this paper we study the fiber F of the rational Jones-Goodwillie character, going from K-theory to negative cyclic homology. We describe F in terms of sheaf cohomology. We show that, for any associative ring A, and n>1, the n-th homotopy group of FA agrees with the -n-th sheaf hypercohomology group of the rational K-theory spectrum on the non-commutative infinitesimal site. The latter is an adaptation of Grothendieck's commutative infinitesimal site. This non-commutative hypercohomology supports a spectral sequence of Brown-Gersten type; we prove degeneracy results for this sequence. We also consider the K-theory of the category of projective modules over the structure sheaf on our site, and show that there is a natural map going from this K-theory and landing in F.

This paper has appeared in J. reine angew. Math., band 503, (1998) 129-160, and has been removed from this server at the request of the author.

Guillermo Cortiñas <>