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

  • Mattia Cavicchi

    LAGA, Institut Galilée, Université Paris 13, F-93430 Villetaneuse, France
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Abstract

We study genus 2 Hilbert-Siegel varieties, i.e. Shimura varieties SKS_K corresponding to the group GSp4,F\mathrm{G}\mathrm{Sp}_{4,F} over a totally real field FF, along with the relative Chow motives λV^\lambda\mathcal{V} of abelian type over SKS_K obtained from irreducible representations VλV_\lambda of GSp4,F\mathrm{G}\mathrm{Sp}_{4,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\lambda, potentially generalisable to other families of Shimura varieties, which characterizes the absence of the 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\mathbb{Q}, whose realizations equal interior (or intersection) cohomology of SKS_K with VλV_{\lambda}-coefficients. We give applications to the construction of homological motives associated to automorphic representations.

Cite this article

Mattia Cavicchi, On the Boundary and Intersection Motives of Genus 2 Hilbert-Siegel Varieties. Doc. Math. 24 (2019), pp. 1033–1098

DOI 10.4171/DM/699