Number Theory Seminar

In classical topology the Hurewicz isomorphism relates singular homology and the abelianized fundamental group of a topological space. A similar relation (with mod-m coefficients) exists for algebraic varieties over algebraically closed fields if singular homology is replaced by Suslin homology and the abelianized fundamental group by its tame étale version. We will present different constructions of such an 'algebraic' Hurewicz isomorphism and then explain how these isomorphisms are related.