Dr. Tobias Schedlmeier (Mainz):
Cartier crystals and perverse constructible étale p-torsion sheaves
Zeit und Ort
Freitag, 20.1.17, 10:15-11:15, Raum 404, Eckerstr. 1
Zusammenfassung
In 2004, Emerton and Kisin established an analogue of the Riemann-Hilbert correspondence for varieties over fields with positive characteristic p. It is an anti-equivalence between the derived categories of so-called unit F-modules and etale constructible \(p\)-torsion sheaves, inducing an anti-equivalence between the abelian categories of unit F-modules and Gabber's perverse sheaves.\n\nIn the talk we explain how this Riemann-Hilbert correspondence can be generalized to singular varieties of positive characteristic which admit an embedding into smooth, F-finite varieties, and introduce the notion of Cartier crystals as a suitable alternative for unit F-modules in this context. Furthermore, we discuss possible further generalizations and the current situation with respect to compatibilities of the correspondence with pull-back and push-forward for certain morphisms.