Tame class field theory for singular varieties over algebraically closed fields

  • Alexander Schmidt

    Universität Heidelberg, Mathematisches Institut, Im Neuenheimer Feld 288, 69120 Heidelberg, Germany
  • Thomas Geisser

    Rikkyo University, Department of Mathematics, 3-34-1 Nishi-Ikebukuro, Toshima-ku, 171-8501 Tokyo, Japan
Tame class field theory for singular varieties over algebraically closed fields cover
Download PDF

This article is published open access.

Abstract

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

Cite this article

Alexander Schmidt, Thomas Geisser, Tame class field theory for singular varieties over algebraically closed fields. Doc. Math. 21 (2016), pp. 91–123

DOI 10.4171/DM/528