Tame class field theory for singular varieties over algebraically closed fields

  • Thomas Geisser

    Rikkyo University Universität Heidelberg Department of Mathematics Mathematisches Institut 3-34-1 Nishi-Ikebukuro Im Neuenheimer Feld 288 Toshima-ku D-69120 Heidelberg Tokyo Japan 171-8501 Deutschland
  • Alexander Schmidt

    Rikkyo University Universität Heidelberg Department of Mathematics Mathematisches Institut 3-34-1 Nishi-Ikebukuro Im Neuenheimer Feld 288 Toshima-ku D-69120 Heidelberg Tokyo Japan 171-8501 Deutschland
Tame class field theory for singular varieties over algebraically closed fields cover
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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

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

DOI 10.4171/DM/528