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Theses

Cohomologie rationnelle du groupe linéaire et extensions de bifoncteurs

Abstract : This thesis aims at obtaining information about the rational cohomology of the general linear group. To tackle this problem, we transpose it in the category of polynomial bifunctors. Indeed, computations are easier in this framework.

We first recall the structure of the category of polynomial bifunctors over an arbitrary commutative ring. We show that bifunctor cohomology computes the rational cohomology of the general linear group (this result was previously know over a field only). Then, we develop techniques to compute bifunctor cohomology. We introduce new effective tools to study Frobenius twists in characteristic p. Finally, we apply these methods to explicit families of bifunctors. In this way, we obtain new results (such as Poincaré series) for rational cohomology with values in classical representations, such as symmetric and divided powers of the twisted Lie algebra of the general linear group.
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https://tel.archives-ouvertes.fr/tel-00289942
Contributor : Antoine Touzé <>
Submitted on : Tuesday, June 24, 2008 - 11:20:21 AM
Last modification on : Monday, March 25, 2019 - 4:52:05 PM
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Antoine Touzé. Cohomologie rationnelle du groupe linéaire et extensions de bifoncteurs. Mathématiques [math]. Université de Nantes, 2008. Français. ⟨tel-00289942⟩

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