**abstract:**
The unramified class field theory of Kato and Saito establishes for smooth varieties $X$ over finite fields an
isomorphism
CH_{0}(X)^{\wedge} \cong \pi_{1}^{ab}(X),
where \wedge denotes profinite completion. This was generalized to the tame fundamental group of quasiprojective varieties by Schmidt and Spiess. The role of the Chow group CH_{0}(X) is taken over by the integral Suslin homology in degree zero. The result fails already for normal, nonregular varieties.

In the talk we explain how to generalize tame class field theory to singular varieties. For connected schemes $X$ of finite type over finite fields we obtain an isomorphism
H_{1}^{{WS}}(X,Z)^{\wedge} \cong \pi_{1}^{{ab,\,tame}}(X).
Here H_{1}^{{WS}}(X, Z) is the Weil-Suslin homology defined by Geisser.
(joint work with Th. Geisser)

Mon 16 Dec, 12:00 - 13:00, Aula Dini

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