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Steklov Institute of Mathematics at St.Petersburg

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PREPRINT 02/2004

A. L. Smirnov
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LEIBNITZ FORMULA IN ALGEBRAIC K-THEORY

This preprint was accepted March 29, 2004

ABSTRACT:
The paper can be considered as an addendum to a paper of Thomason and Throbaugh
where K-theory of algebraic varieties is equipped with relative K-groups.
It is proved that this enriched K-theory satisfies the Panin-Smirnov axioms for
ring cohomology theories of algebraic varieties. In particular it is proved that the Leibnitz
formula, describing an interaction between a multiplication and
a differential, holds in this case. A language of symmetric spectra
and of monoidal model categories is used.

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