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

Ryan Reich

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

Received 14 May 2010. Received in revised form 9 July 2010.

Watch a lecture on this article by the author.

DOI: 10.5427/jsing.2010.1g

Add a reference to this article to your citeulike library.

Abstract:

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.

Keywords:

perverse sheaves, nearby cycles, vanishing cycles, gluing

Mathematical Subject Classification:

32B15, 32C35, 32C18, 32B10

Author(s) information:

Ryan Reich
email: ryanr@math.harvard.edu