Perverse sheaves and the reductive Borel-Serre compactification

zbMATH Open1386.14078arXiv1612.01207MaRDI QIDQ4597187

Publication date: 11 December 2017

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).

Full work available at URL: https://arxiv.org/abs/1612.01207

zbMATH Keywords

intersection cohomology locally symmetric space perverse sheaves Borel-Serre compactification Baily-Borel compactification

Mathematics Subject Classification ID

Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) (32M15) Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) (14F43) Homology and cohomology of homogeneous spaces of Lie groups (57T15) Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) (18F20) Compactifications; symmetric and spherical varieties (14M27)