Un isomorphisme de Suslin

Kelly, Shane

Bulletin de la Société Mathématique de France, Tome 146 (2018) no. 4, pp. 633-647

Dans cette note on constate qu’on peut enlever l’hypothèse de la résolution des singularités de l’isomorphisme construit par Suslin entre la cohomologie étale à supports compacts et les groupes de Chow supérieurs de Bloch. On démontre de plus que l’on peut obtenir cet isomorphisme à partir de la réalisation étale d’Ivorra.

In this note we observe that we can remove the resolution of singularities hypothesis from the isomorphism constructed by Suslin between étale cohomology with compact supports and Bloch’s higher Chow groups. Moreover, we show that this isomorphism can be obtained from Ivorra’s étale realisation functor.

Classification : 14F20, 19E15, 14C15
Mots-clés : Cohomologie étale, cycles algébriques, cohomologie motivique, groups de Chow supérieurs
Keywords: Étale cohomology, algebraic cycles, motivic cohomology, higher Chow groups

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