Mathematics Seminar
Date: Wednesday, 06 March 2024
Time: 02:30 - 03:20 PM
Venue: Seminar hall
Geometric realization of perverse filtration
Ankit Rai
Chennai Mathematical Institute.
06-03-24

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Abstract

Perverse sheaves are certain complexes of constructible sheaves invented by Goresky-MacPherson around 1983. This talk will be centered around the topic of (middle) perverse sheaves and t-structure(s) on the derived category of constructible sheaves on an algebraic variety X defined over a field k.

A t-structure (as above) gives rise to a sequence of truncation functors which equips K, a complex of constructible sheaves on an algebraic variety X, with a filtration which will be called as the perverse filtration. This in turn induces a filtration on the (hyper) cohomology of the complex K. In 2010, deCataldo-Migliorini proved a result which explains this filtration via geometry. In a work joint with K. V. Shuddhodan, we show that their result can be upgraded to an equality at the level of sheaves and is a corollary of the t-exactness of certain Brylinski-Radon transforms.