Seminar by Masaharu Kaneda (Osaka City University)

Title: Representation theory of $F_*\mathcal{O}_{G/P}$

2013.11.25 | Christine Dilling

 Date Wed 24 Mar Time 14:15 — 15:15 Location Aud. D3

Abstract:

In the complex projective spaces Beilinson found 30 years ago a family of invertible sheaves such that the bounded derived category of coherent sheaves is equivalent to the bounded derived category of finite dimensional right modules over the endomorphism ring of the direct sum of those invertible sheaves.

Subsequently, Kapranov found a family of coherent sheaves on the flag varieties of the general linear groups and on the quadrics to realize the equivalence likewise .

Writing the homogeneous projective variety as G/P, in recent joint works with Ye Jiachen we have extended the above list of varieties to include the cases of reductive groups G of rank 2. All these sheaves are defined over the ring of integers and we are hoping they apper by base change in the Frobenius direct image of the structure sheaf of the variety. We will explain our constructin of the sheaves using the modular representation theory of G.

Seminar