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Weighted complexes on Baily-Borel compactifications: the case of Siegel varieties. (Complexes pondérés sur les compactifications de Baily-Borel: le cas des variétés de Siegel.) (English) Zbl 1225.11073
Summary: We calculate the trace of a Hecke correspondence 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 R. 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 [Math. Ann. 292, No. 2, 197–240 (1992; Zbl 0748.14008)]. 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 M. Goresky, G. Harder and R. MacPherson [Invent. Math. 116, 139–213 (1994; Zbl 0849.11047)].

MSC:
11F75 Cohomology of arithmetic groups
11G18 Arithmetic aspects of modular and Shimura varieties
14G35 Modular and Shimura varieties
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