Chandrasekhar Hall

Geometric realization of perverse filtration

Dr. Ankit Rai

CMI

Perverse sheaves are certain complexes of constructible sheaves invented by Goresky-MacPherson in 1983. This talk will be centered around the topic of (middle) perverse sheaves and more generally on t-structure(s) on derived category of constructible sheaves on an algebraic variety X defined over a field k. A t-structure gives rise to truncation functors and hence a cohomology theory which takes values in the abelian category of perverse sheaves. A complex K of constructible sheaves on X can be filtered using these truncation functors which 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 recent work 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 certain t-exactness of a certain Brylinski-Radon transforms.