Complexes pondérés sur les compactifications de Baily-Borel: Le cas des variétés de Siegel

Morel, Sophie

doi:10.1090/S0894-0347-06-00538-8

Complexes pondérés sur les compactifications de Baily-Borel: Le cas des variétés de Siegel
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by Sophie Morel

J. Amer. Math. Soc. 21 (2008), 23-61

DOI: https://doi.org/10.1090/S0894-0347-06-00538-8

Published electronically: June 9, 2006

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Abstract:

In this work, we calculate the trace of a Hecke correspondance composed with a power of the Frobenius endomorphism on the fibre of the intersection complexes of the Baily-Borel compactification of a Siegel modular variety. Our main tool is Pink’s theorem about the restriction to the strata of the Baily-Borel compactification of the direct image of a local system on the Shimura variety. To use this theorem, we give a new construction of the intermediate extension of a pure perverse sheaf as a weight truncation of the full direct image. More generally, we are able to define analogs in positive characteristic of the weighted cohomology complexes introduced by Goresky, Harder and MacPherson.

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Lefschetz-Verdier trace formula and a generalization of a theorem of Fujiwara