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6 papers
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 Lie algebra cohomology of SU(2,1) and Eisenstein classes on Picard surfaces
Jitendra Bajpai, Mattia Cavicchi
We consider Picard surfaces, locally symmetric varieties attached to the Lie group SU(2,1), and we construct explicit differential forms on representing Eisenstein clas…
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…
Bloch-Beilinson conjectures for Hecke characters and Eisenstein cohomology of Picard surfaces
Jitendra Bajpai, Mattia Cavicchi
We consider certain families of Hecke characters over a quadratic imaginary field . According to the Bloch-Beilinson conjectures, the order of vanishing of the -function…
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…