Kay Rülling (Universität Wuppertal)

Abstract:
On noetherian F-finite \F_p-schemes, the class of constructible étale \Z/p^n-sheaves contains the constant sheaf \Z/p^n and is stable under higher direct images along proper maps.
Contrary to the \ell-torsion situation the twisted sheaves \Z/p^n(j) are not constructible.
In this talk we introduce dual constructible p-torsion complexes, which contain only the top twisted sheaves, are stable under higher direct images along arbitrary separated morphisms of finite type, and are dual under Kato duality to the constructible complexes of \Z/p^n-sheaves. The proof uses a Riemann-Hilbert style equivalence between the derived category of Cartier crystals introduced by Blickle-Böckle and the category of dual constructible complexes, which by an argument involving Grothendieck and Kato-duality is reduced to a version of the classical Riemann-Hilbert Theorem for \F_p-sheaves by Emerton-Kisin and Böckle-Pink. This is joint work with Jefferson Baudin.