Notes on Beilinson's "How to glue perverse sheaves"

Details Notes on Beilinson's "How to glue perverse sheaves" Notes on Beilinson's "How to glue perverse sheaves"

2010-02-08

arxiv.org/abs/1002.1686v4

Journal of Singularities, volume 1 (2010) pp. 94--115

Mathematics

Algebraic Geometry

22 pages

Scientific paper

The titular, foundational work of Beilinson not only gives a technique for gluing perverse sheaves but also implicitly contains constructions of the nearby and vanishing cycles functors of perverse sheaves. These constructions are completely elementary and show that these functors preserve perversity and respect Verdier duality on perverse sheaves. The work also defines a new, "maximal extension" functor, which is left mysterious aside from its role in the gluing theorem. In these notes, we present the complete details of all of these constructions and theorems.

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