A Uniform Identification of Stable Sheaf Cohomology

TL;DR

This paper proves an isomorphism of arithmetic complexes related to stable sheaf cohomology on flag varieties, extending previous conjectures and unifying the identification across different complexes over the integers.

Contribution

It establishes a uniform isomorphism of complexes conjectured by Gao, Raicu, and VandeBogert, generalizing stable sheaf cohomology identifications to integer-based projective spaces.

Findings

Proved an isomorphism of complexes over integer-valued polynomial rings.

Unified the stable sheaf cohomology identification for hook and two-column Schur functors.

Extended results to projective spaces over the integers.

Abstract

This paper considers generalizations of certain arithmetic complexes appearing in the work of Raicu and VandeBogert in connection with the study of stable sheaf cohomology on flag varieties. Defined over the ring of integer valued polynomials, we prove an isomorphism of these complexes as conjectured by Gao, Raicu, and VandeBogert. In particular, this shows that a previously made identification between the stable sheaf cohomology of hook and two column partition Schur functors applied to the cotangent sheaf of projective space can be made to be uniform with respect to these complexes. These results are extended to the projective space defined over the integers.