Geodesic
On the Boundary and Intersection Motives of Genus 2 Hilbert-Siegel Varieties
Documenta mathematica, Tome 24 (2019), pp. 1033-1098
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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 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.
DOI : 10.4171/dm/699
Classification : 11F46, 11F70, 11G18, 14G35
Mots-clés : Shimura varieties, Hilbert-Siegel varieties, boundary motive, intersection motive, weight structures, motives for Hilbert-Siegel modular forms 
@article{10_4171_dm_699,
     author = {Mattia Cavicchi},
     title = {On the {Boundary} and {Intersection} {Motives} of {Genus} 2 {Hilbert-Siegel} {Varieties}},
     journal = {Documenta mathematica},
     pages = {1033--1098},
     year = {2019},
     volume = {24},
     doi = {10.4171/dm/699},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/699/}
}
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Mattia Cavicchi. On the Boundary and Intersection Motives of Genus 2 Hilbert-Siegel Varieties. Documenta mathematica, Tome 24 (2019), pp. 1033-1098. doi: 10.4171/dm/699

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