[Les six opérations de Grothendieck sur les faisceaux o-minimaux]
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.
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@article{CRMATH_2014__352_6_455_0,
author = {Edmundo, M\'ario J. and Prelli, Luca},
title = {The six {Grothendieck} operations on o-minimal sheaves},
journal = {Comptes Rendus. Math\'ematique},
pages = {455--458},
publisher = {Elsevier},
volume = {352},
number = {6},
year = {2014},
doi = {10.1016/j.crma.2014.03.021},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2014.03.021/}
}
TY - JOUR AU - Edmundo, Mário J. AU - Prelli, Luca TI - The six Grothendieck operations on o-minimal sheaves JO - Comptes Rendus. Mathématique PY - 2014 SP - 455 EP - 458 VL - 352 IS - 6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2014.03.021/ DO - 10.1016/j.crma.2014.03.021 LA - en ID - CRMATH_2014__352_6_455_0 ER -
%0 Journal Article %A Edmundo, Mário J. %A Prelli, Luca %T The six Grothendieck operations on o-minimal sheaves %J Comptes Rendus. Mathématique %D 2014 %P 455-458 %V 352 %N 6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2014.03.021/ %R 10.1016/j.crma.2014.03.021 %G en %F CRMATH_2014__352_6_455_0
Edmundo, Mário J.; Prelli, Luca. The six Grothendieck operations on o-minimal sheaves. Comptes Rendus. Mathématique, Tome 352 (2014) no. 6, pp. 455-458. doi : 10.1016/j.crma.2014.03.021. http://www.numdam.org/articles/10.1016/j.crma.2014.03.021/
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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.
