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

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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