We study genus 2 Hilbert-Siegel varieties, i.e. Shimura varieties corresponding to the group over a totally real field , along with the relative Chow motives of abelian type over obtained from irreducible representations of . 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 , 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 , whose realizations equal interior (or intersection) cohomology of with -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. 1033–1098DOI 10.4171/DM/699