Algebra Seminar: Hardesty -- Co-t-structures on derived categories of coherent sheaves and the cohomology of tilting modules

William Hardesty (University of Sydney) 

Friday 20 September, 12-1pm, Place: Carslaw 375 

Title: Co-t-structures on derived categories of coherent sheaves and the cohomology of
tilting modules 

Abstract: Since the mid 1990s, understanding the "Frobenius kernel cohomology" of
tilting modules has been an important area of research in modular representation
theory.  Another important area of research, which is sometimes called "coherent
Springer theory", involves the study of derived equivariant coherent sheaves on the
nilpotent cone and the Springer resolution.  Due to the work of Achar and Riche, we now
know that both of these topics are related by a derived equivalence.  In particular, the
cohomology of a tilting module is given by the global sections of a corresponding
(derived) equivariant coherent sheaf on nilpotent cone.  In this talk, I will present
recent joint work with Pramod Achar, where we intrinsically characterize these sheaves
as the indecomposable objects in the “co-heart” of a certain non-trivial
"co-t-structure" on the equivariant derived category of coherent sheaves on the
nilpotent cone.  I will also discuss some additional exciting progress that we have
towards the study of tilting module cohomology by employing the framework of
co-t-structures.  This includes a new proof of the "Humphreys conjecture on support
varieties" for SL_n as well as a conjecture which alternatively characterizes these
sheaves as extensions of “tilting bundles” on nilpotent orbits.