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The motivic Hecke algebra for PEL Shimura varieties
Mattia Cavicchi
We construct a motivic lift of the action of the Hecke algebra on the cohomology of PEL Shimura varieties . To do so, when is associated with a reductive algebraic group…
Relative and absolute Lefschetz standard conjectures for some Lagrangian fibrations
Giuseppe Ancona, Mattia Cavicchi, Robert Laterveer +1
We show that the hyper-Kähler varieties of OG10-type constructed by Laza-Saccà-Voisin (LSV) verify the Lefschetz standard conjecture. This is an application of a more general resul…
Motivic decompositions of families with Tate fibers: smooth and singular cases
Mattia Cavicchi, Frédéric Déglise, Jan Nagel
We apply Wildeshaus's theory of motivic intermediate extensions to the motivic decomposition conjecture, formulated by Deninger-Murre and Corti-Hanamura. We first obtain a general…
On the boundary and intersection motives of genus 2 Hilbert-Siegel varieties
Mattia Cavicchi
We study genus 2 Hilbert-Siegel varieties, i.e. Shimura varieties corresponding to the group $\mbox{GSp}_{4,F}$ over a totally real field , along with the relative Chow mo…