Un isomorphisme de Suslin

TL;DR

This paper demonstrates that the isomorphism between étale cohomology with compact support and Bloch's higher Chow groups, originally established by Suslin, can be achieved without assuming resolution of singularities, using Ivorra's realization functor.

Contribution

It removes the resolution of singularities hypothesis from Suslin's isomorphism and employs Ivorra's realization functor for its construction.

Findings

The isomorphism holds over algebraically closed fields without resolution of singularities.

Ivorra's realization functor provides an alternative construction of the isomorphism.

The result broadens the applicability of Suslin's isomorphism in algebraic geometry.

Abstract

In this note we observe that we can remove the hypothesis of resolution of singularities from the isomorphism constructed by Suslin between the \'etale cohomology with compact support and Bloch's higher Chow groups over an algebraically closed field. We also show that this isomorphism can be obtained using Ivorra's realisation functor.