Tame Class Field Theory for Singular Varieties over Algebraically Closed Fields

Thomas Geisser; Alexander Schmidt

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arXiv · 1309.4068

Tame Class Field Theory for Singular Varieties over Algebraically Closed Fields

Thomas Geisser·Alexander Schmidt

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Abstract

Let X be a separated scheme of finite type over an algebraically closed field k and let m be a natural number. By an explicit geometric construction using torsors we construct a pairing between the first mod m Suslin homology and the first mod m tame etale cohomology of X. We show that the induced homomorphism from the mod m Suslin homology to the abelianized tame fundamental group of X mod m is surjective. It is an isomorphism of finite abelian groups if (m, char(k)) = 1, and for general m if resolution of singularities holds over k.

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Thomas Geisser, Alexander Schmidt. 2013-09-16. Tame Class Field Theory for Singular Varieties over Algebraically Closed Fields. https://arxiv.org/abs/1309.4068

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