# Geometry of the flag variety and $$G_1$$ T-Verma modules

Algebra/Geometry/Topology Seminar

#### by Kaneda Masaharu

Institution: Osaka City University
Date: Fri 19th August 2011
Time: 3:15 PM
Location: 213 Richard Berry

Abstract: Let PC be a complex homogeneous projective variety. Write PC = GC /pC with a complex reductive group GC and a parabolic subgroup pC of GC . These groups are deﬁned over Z and have counterparts G and p in positive characteristic. Let G1 be the kernel of the Frobenius endomorphism of G, which corresponds to the Lie algebra of GC , and T a maximal torus of p. We will present a recipe we hope
to construct a complete strongly exceptional sequence of coherent sheaves on X from parabolically induced G1 T -Verma modules.