Perverse sheaves and the reductive Borel-Serre compactification

2016/12/04 by Saper, Leslie
#Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1612.01207

Abstract

We briefly introduce the theory of perverse sheaves with special attention to the topological situation where strata can have odd dimension. This is part of a project to use perverse sheaves on the topological reductive Borel-Serre compactification of a Hermitian locally symmetric space as a tool to study perverse sheaves on the Baily-Borel compactification, a projective algebraic variety. We sketch why the decomposition theorem holds for the natural map between the reductive Borel-Serre and the Baily-Borel compactifications. We demonstrate how to calculate extensions of simple perverse sheaves on the reductive Borel-Serre compactification and illustrate with the example of Sp(4,R).

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