Holmstrom Perverse sheaves

BBD

Dimca: Sheaves in topology. In Homol alg folder

http://www.ncatlab.org/nlab/show/perverse+sheaf

arXiv:1004.2983 What is a perverse sheaf? from arXiv Front: math.AG by Mark Andrea de Cataldo, Luca Migliorini Three-page article on the notion of perverse sheaf to appear in the “What is?” series in the Notices of the AMS.

http://mathoverflow.net/questions/1675/how-to-do-computations-using-the-decomposition-theorem-for-perverse-sheaves

http://mathoverflow.net/questions/74116/crystalline-analogue-of-perverse-sheaves

Kiehl and Weissauer: Weil conj, perverse sheaves, etc

For some notes on perverse sheaves and vanishing cycles, see folder AG/Perverse sheaves.

http://mathoverflow.net/questions/55790/bad-behaviour-of-perverse-sheaves-over-general-bases

http://mathoverflow.net/questions/49797/the-conjectural-relation-between-mixed-motivic-sheaves-and-the-perverse-t-structu

arXiv:1002.1686 Notes on Beilinson’s “How to glue perverse sheaves” from arXiv Front: math.CT by Ryan Reich 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.

math/0005152 Perverse coherent sheaves (after Deligne) from arXiv Front: math.AG by Roman Bezrukavnikov This note is mostly an exposition of an unpublished result of Deligne, which introduces an analogue of perverse $t$-structure on the derived category of coherent sheaves on a Noetherian scheme with a dualizing complex. Construction extends to the category of coherent sheaves equivariant under an action of an algebraic group; though proof of the general statement in this case does not require new ideas, it provides examples (such as sheaves on the nilpotent cone of a semi-simple group equivariant under the adjoint action) where construction of coherent “intersection cohomology” sheaves works.

math/9908107 Notes on Perverse Sheaves and Vanishing Cycles from arXiv Front: math.AG by David B. Massey 1 person liked this A working mathematician’s summary of many results on the derived category, perverse sheaves, and vanishing cycles. This is the February 2010 version.

nLab page on Perverse sheaves