The six Grothendieck operations on o-minimal sheaves

Mário J. Edmundo; Luca Prelli

doi:10.1016/j.crma.2014.03.021

Logic/Geometry

The six Grothendieck operations on o-minimal sheaves
[Les six opérations de Grothendieck sur les faisceaux o-minimaux]

Présenté par : the Editorial Board

Mário J. Edmundo ^1,² ; Luca Prelli ²

¹ Universidade Aberta, Campus do Tagus Park, Edifício Inovação I, Av. Dr. Jaques Delors, 2740-122 Porto Salvo, Oeiras, Portugal
² CMAF Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal

Comptes Rendus. Mathématique, Volume 352 (2014) no. 6, pp. 455-458.

Résumé
Abstract

Dans cette note, nous esquissons notre travail sur le formalisme des six opérations de Grothendieck sur les faisceaux o-minimaux. En tant qu'application à la théorie des groupes définissables, nous montrons que la cohomologie d'un groupe définissablement compact avec coefficients dans un corps est une algèbre de Hopf connexe, bornée, de type fini.

In this note, we report on our work on the formalism of the Grothendieck six operations on o-minimal sheaves. As an application to the theory of definable groups, we see that the cohomology of a definably compact group with coefficients in a field is a connected, bounded, Hopf algebra of finite type.

Reçu le : 2013-11-30
Accepté le : 2014-03-26
Publié le : 2014-04-16

DOI : 10.1016/j.crma.2014.03.021

Affiliations des auteurs :

Mário J. Edmundo ^{1, 2} ; Luca Prelli ²

¹ Universidade Aberta, Campus do Tagus Park, Edifício Inovação I, Av. Dr. Jaques Delors, 2740-122 Porto Salvo, Oeiras, Portugal
² CMAF Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal

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Mário J. Edmundo; Luca Prelli. The six Grothendieck operations on o-minimal sheaves. Comptes Rendus. Mathématique, Volume 352 (2014) no. 6, pp. 455-458. doi : 10.1016/j.crma.2014.03.021. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.03.021/

Bibliographie
Cité par

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Cité par Sources :

^☆ The first author was supported by Fundação para a Ciência e a Tecnologia, Financiamento Base 2008 – ISFL/1/209. The second author is a member of the Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM) and was supported by Marie Curie grant PIEF-GA-2010-272021. This work is part of the FCT project PTDC/MAT/101740/2008.

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