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Article Dans Une Revue Documenta Mathematica Année : 2019

On the Boundary and Intersection Motives of Genus 2 Hilbert-Siegel Varieties

Résumé

We study genus 2 Hilbert-Siegel varieties, i.e. Shimura varieties SK corresponding to the group GSp4,F over a totally real field F , along with the relative Chow motives λV of abelian type over SK obtained from irreducible representations Vλ of GSp4,F . We analyse the weight filtration on the degeneration of such motives at the boundary of the Baily-Borel compactification and we find a criterion on the highest weight λ , potentially generalisable to other families of Shimura varieties, which characterizes the absence of the \textit{middle weights} 0 and 1 in the corresponding degeneration. Thanks to Wildeshaus' theory, the absence of these weights allows us to construct Hecke-equivariant Chow motives over Q , whose realizations equal interior (or intersection) cohomology of SK with Vλ -coefficients. We give applications to the construction of homological motives associated to automorphic representations.
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Dates et versions

hal-03965880 , version 1 (31-01-2023)

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Mattia Cavicchi. On the Boundary and Intersection Motives of Genus 2 Hilbert-Siegel Varieties. Documenta Mathematica, 2019, 24, pp.1033-1098. ⟨10.25537/dm.2019v24.1033-1098⟩. ⟨hal-03965880⟩
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