A Uniform Identification of Stable Sheaf Cohomology

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.