Geodesic
Tame class field theory for singular varieties over algebraically closed fields
Documenta mathematica, Tome 21 (2016), pp. 91-123
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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 étale 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.
DOI : 10.4171/dm/528
Classification : 14C25, 14F35, 14F43
Mots-clés : Suslin homology, higher dimensional class field theory, tame fundamental group 
@article{10_4171_dm_528,
     author = {Alexander Schmidt and Thomas Geisser},
     title = {Tame class field theory for singular varieties over algebraically closed fields},
     journal = {Documenta mathematica},
     pages = {91--123},
     year = {2016},
     volume = {21},
     doi = {10.4171/dm/528},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/528/}
}
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Alexander Schmidt; Thomas Geisser. Tame class field theory for singular varieties over algebraically closed fields. Documenta mathematica, Tome 21 (2016), pp. 91-123. doi: 10.4171/dm/528

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