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Theses

Sur le motif intérieur de certaines variétés de Shimura : le cas des variétés de Picard

Abstract : Picard varieties are Shimura varieties associated to the group of unitary similitudes of an hermitian space of dimension 3 over a CM eld. They parametrize isomorphism classes of abelian varieties with some additional data. In particular, there exists a universal abelian variety over a Picard variety and more generally Kuga-Sato families. Cohomology groups are attached to these varieties. Automorphic representations can be found in cohomology groups, more precisely in interior cohomology groups. Following Langlands' program, these representations correspond conjecturally to motives. The main result of this thesis is the construction of direct factors of the interior motive of certain Kuga-Sato families over a Picard variety, meaning a motivic analogue of interior cohomology. To prove this, we study the weights of the boundary motive of such families. We deduce from this the existence of a motive associated to certain automorphic representations.
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Guillaume Cloitre. Sur le motif intérieur de certaines variétés de Shimura : le cas des variétés de Picard. Théorie des nombres [math.NT]. Université Sorbonne Paris Cité, 2017. Français. ⟨NNT : 2017USPCD033⟩. ⟨tel-01901103⟩

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