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arXiv · 1807.08690

Dualit\'e de Koszul formelle et th\'eorie des repr\'esentations des groupes alg\'ebriques r\'eductifs en caract\'eristique positive

Pramod N. Achar·Simon Riche
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Abstract

In this survey paper, we present the broad outlines of the proof of a character formula for tilting representations of reductive algebraic groups in positive characteristic, obtained partly in collaboration with several other authors. A unifying theme for a number of steps of this proof is the notion of "formal Koszul duality." We explain this notion and discuss some applications. ----- Dans cet article nous pr\'esentons les grandes lignes de la preuve d'une formule de caract\`eres pour les repr\'esentations basculantes des groupes alg\'ebriques r\'eductifs sur un corps de caract\'eristique positive, obtenue partiellement en collaboration avec plusieurs auteurs. Nous unissons les diff\'erentes \'etapes de cette preuve dans la notion de "dualit\'e de Koszul formelle", et en pr\'esentons quelques applications.

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BibTeXRIS

Pramod N. Achar, Simon Riche. 2018-07-23. Dualit\'e de Koszul formelle et th\'eorie des repr\'esentations des groupes alg\'ebriques r\'eductifs en caract\'eristique positive. https://arxiv.org/abs/1807.08690

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