Abstract Alexander Samokhin

T-structures on the derived categories of coherent sheaves on flag varieties arising from Frobenius morphism

Abstract: In this talk, we are going to discuss two problems related to the flag variety G/B of a semi-simple algebraic group G: constructing tilting equivalences for the derived category of coherent sheaves, and describing cohomology vanishing patterns of line bundles in characteristic p. The bridge between the two topics is carried out by the study of Frobenius morphism on G/B. In particular, we will explain in detail the example of the groups of rank two.