Decompositions of Frobenius pushforwards of vector bundles on partial flag varieties

Alexander Samokhin (IITP Moscow)

Wednesday 23rd January 16:00-17:00 Maths 311B

Abstract

In this talk, I will explain how to explicitly determine
indecomposable summands of Frobenius pushforwards of vector bundles on
(partial) flag varieties, provided that there exists a special
semi-orthogonal decomposition in the derived category of coherent
sheaves. I will then show how this can be applied to calculating
cohomology of line bundles on flag varieties in characteristic p, and
work out in detail the example of a partial flag variety which is the
projectivization of the minimal nilpotent orbit in type A. Time
permitting, we will discuss related questions, e.g., the finite
F-representation type property, in the context of that example.

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