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

Presented by: 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.

Abstract
Résumé

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.

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.

Received: 2013-11-30
Accepted: 2014-03-26
Published online: 2014-04-16

DOI: 10.1016/j.crma.2014.03.021

Author's affiliations:

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/

References
Cited by

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Cited by 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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