2025/03/03 by Robert Cass, Cass, Robert, João Lourenço +1
Mathematics · #Algebraic structures and combinatorial models #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2503.01796
We characterize Cohen--Macaulay and φ-rational perfect schemes in terms of their perverse étale mod p sheaves. Using inversion of adjunction, we prove that sufficiently small Schubert varieties in the Witt affine flag variety are perfections of globally +-regular varieties, and hence they are φ-rational. Our methods apply uniformly to all affine Schubert varieties in equicharacteristic, as well as classical Schubert varieties, thereby answering a question of Bhatt. As a corollary, we deduce that scheme-theoretic local models always have φ-split special fiber.