Algebraic Geometry Seminar
Ethan Reed
University of Notre Dame
Stable Sheaf Cohomology and an Isomorphism Theorem for Arithmetic Complexes
Abstract: In characteristic 0, the sheaf cohomology groups for line bundles on the full flag variety are given by the Borel-Weil-Bott Theorem. However, in positive characteristic a full description is not known. I will discuss some progress in positive characteristic including recent stabilization results of Raicu and Vandebogert. Further, Raicu and Vandebogert computed special cases of these stable cohomology groups using certain arithmetic complexes (arithmetic in the sense that they are defined over the integers). I will then discuss joint work with Luca Fiorindo, Shahriyar Roshan-Zamir, and Hongmiao Yu in which we prove an isomorphism of generalizations of these complexes defined over the ring of integer valued polynomials as conjectured by Gao, Raicu, and Vandebogert. In particular, this gives a more conceptual proof of an identification between the stable sheaf cohomology groups of hook and two column partition Schur functors applied to the cotangent sheaf of projective space.
Monday January 29, 2024 at 3:00 PM in 636 SEO