Tuesday, November 2, 15:00

Pramod Achar (Louisiana State University)
Co-t-structures, coherent sheaves, and the cohomology of tilting modules for algebraic groups.
(Two talks.)

Abstract:
In the first part of the talk, I will give general background on co-t-structures (or the equivalent language of silting subcategories), including elementary examples, and a procedure for constructing co-t-structures and co-t-structures in terms of the notion of (co-)quasi-exceptional sets. In particular, this procedure can be applied to the derived category of coherent sheaves on the nilpotent cone of a reductive algebraic group. I will explain the connection between this co-t-structure and 20-year-old conjecture on Humphreys on tilting modules for algebraic groups.
In the second part of the talk, I will discuss a second, seemingly unrelated construction of a co-t-structure on the same derived category. A surprisingly easy argument shows that the two co-t-structures coincide, and this implies Humphreys's conjecture. This is joint work with W. Hardesty (and partly also with S. Riche).