Kisin, MarkCass, Robert Alan2021-07-1320212021-05-112021-05Cass, Robert Alan. 2021. Perverse mod p Sheaves on Affine Flag Varieties. Doctoral dissertation, Harvard University Graduate School of Arts and Sciences.28498071https://nrs.harvard.edu/URN-3:HUL.INSTREPOS:37368323We prove a mod p analogue of the geometric Satake equivalence and we give a geometric construction of central elements in affine mod p Hecke algebras. To accomplish these goals we apply techniques from F-singularities to the theory of perverse mod p sheaves on schemes in characteristic p. Along the way we prove new results about the F-singularities of affine Schubert varieties and equal characteristic analogues of local models of Shimura varieties.application/pdfenaffine Schubert varietiesF-singularitiesgeometric SatakeHecke algebraslocal modelsperverse sheavesMathematicsThesis or Dissertation2021-07-130000-0003-2242-5758