Comparing motives of smooth algebraic varieties

Garkusha, Grigory

doi:10.1016/j.crma.2018.11.006

Homological algebra/Algebraic geometry

Comparing motives of smooth algebraic varieties
[Comparaison des motifs de variétés algébriques lisses]

Présenté par : Claire Voisin

Garkusha, Grigory ¹

¹ Department of Mathematics, Swansea University, Fabian Way, Swansea SA1 8EN, UK

Comptes Rendus. Mathématique, Tome 356 (2018) no. 11-12, pp. 1100-1105.

Résumé
Abstract

Étant donné un corps parfait de caractéristique exponentielle e, nous montrons que les Cor-, $K_{0}^{\oplus}$ -, $K_{0}$ - et $K_{0}$ -motifs des variétés algébriques lisses à coefficients dans $Z [1 / e]$ sont localement quasi isomorphes deux à deux. De plus, nous démontrons que leurs catégories triangulées de motifs à coefficients dans $Z [1 / e]$ sont équivalentes. Une application est donnée pour la suite spectrale motivique bivariante.

Given a perfect field of exponential characteristic e, the Cor-, $K_{0}^{\oplus}$ -, $K_{0}$ - and $K_{0}$ -motives of smooth algebraic varieties with $Z [1 / e]$ -coefficients are shown to be locally quasi-isomorphic to each other. Moreover, it is proved that their triangulated categories of motives with $Z [1 / e]$ -coefficients are equivalent. An application is given for the bivariant motivic spectral sequence.

Reçu le : 2017-10-10
Accepté le : 2018-11-08
Publié le : 2018-11-01

DOI : 10.1016/j.crma.2018.11.006

Affiliations des auteurs :

Garkusha, Grigory ¹

¹ Department of Mathematics, Swansea University, Fabian Way, Swansea SA1 8EN, UK

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Garkusha, Grigory. Comparing motives of smooth algebraic varieties. Comptes Rendus. Mathématique, Tome 356 (2018) no. 11-12, pp. 1100-1105. doi : 10.1016/j.crma.2018.11.006. http://archive.numdam.org/articles/10.1016/j.crma.2018.11.006/

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