Geodesic
Tame class field theory for singular varieties over algebraically closed fields
Documenta mathematica, Tome 21 (2016), pp. 91-123.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 $k$.
Classification : 14F35, 14F43, 14C25
Keywords: Suslin homology, higher dimensional class field theory, tame fundamental group 
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     author = {Geisser, Thomas and Schmidt, Alexander},
     title = {Tame class field theory for singular varieties over algebraically closed fields},
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     publisher = {mathdoc},
     volume = {21},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2016__21__a40/}
}
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Geisser, Thomas; Schmidt, Alexander. Tame class field theory for singular varieties over algebraically closed fields. Documenta mathematica, Tome 21 (2016), pp. 91-123. http://geodesic.mathdoc.fr/item/DOCMA_2016__21__a40/