Tame class field theory of arithmetic schemes
by
Alexander Schmidt
University of Heidelberg

The tamely ramified abelian coverings of a smooth, quasiprojective variety over finite field can be described in terms of its 0th singular (Suslin) homology. This extends the unramified class field theory of Kato and Saito for smooth, projective varieties over finite fields to the quasiprojective case. We explain this result (joint work with M. Spieß) and give an overview on the current state of the expected analogous result for regular schemes of finite type over the spectrum of the integers.

Date received: February 23, 2001