Rigidity theorem for presheaves with \Omega-transfers

TL;DR

This paper proves a rigidity theorem for homotopy invariant presheaves with -transfers, extending the classical Suslin rigidity theorem to a broader class of cohomology theories including algebraic K-theory and cobordism.

Contribution

It establishes a new rigidity theorem for presheaves with -transfers, generalizing previous results and encompassing important theories like K-theory and algebraic cobordism.

Findings

Proves rigidity theorem for presheaves with -transfers

Includes K-functor and algebraic cobordism as special cases

Extends classical Suslin rigidity results

Abstract

In 1983 A. Suslin proved the Quillen-Lichtenbaum conjecture about algebraic K-theory of algebraically closed fields. The proof was based on a theorem called the Suslin rigidity theorem. In the present paper we prove the rigidity theorem for homotopy invariant presheaves with \Omega-transfers, introduced by I. Panin. This type of presheaves includes the K-functor and algebraic cobordism of M. Levine and F. Morel. Keywords: rigidity theorem, presheaves with transfers, cohomology theories. MSC2000: 14F43