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.
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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 = {https://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 - https://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 https://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, Volume 352 (2014) no. 6, pp. 455-458. doi : 10.1016/j.crma.2014.03.021. https://www.numdam.org/articles/10.1016/j.crma.2014.03.021/
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☆ 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.
