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arXiv · 1612.01207

Perverse sheaves and the reductive Borel-Serre compactification

Leslie Saper
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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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Leslie Saper. 2016-12-04. Perverse sheaves and the reductive Borel-Serre compactification. https://arxiv.org/abs/1612.01207

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