2018/06/26 by Sophie Morel, Morel, Sophie
Mathematics · #11F75 (primary) #11G18 #14G35 (secondary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1806.09909
openalex publication_date 2018/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we calculate the trace of a Hecke correspondance composed with\na power of the Frobenius endomorphism on the fibre of the intersection\ncomplexes of the Baily-Borel compactification of a Siegel modular variety. Our\nmain tool is Pink's theorem about the restriction to the strata of the\nBaily-Borel compactification of the direct image of a local system on the\nShimura variety. To use this theorem, we give a new construction of the\nintermediate extension of a pure perverse sheaf as a weight truncation of the\nfull direct image. More generally, we are able to define analogs in positive\ncharacteristic of the weighted cohomology complexes introduced by Goresky,\nHarder and MacPherson.\n