ﻻ يوجد ملخص باللغة العربية
Inspired by a theorem of Bhatt-Morrow-Scholze, we develop a stacky approach to crystals and isocrystals on Frobenius-smooth schemes over F_p . This class of schemes goes back to Berthelot-Messing and contains all smooth schemes over perfect fields of characteristic p. To treat isocrystals, we prove some descent theorems for sheaves of Banachian modules, which could be interesting in their own right.
This work is dedicated to a new completely algebraic approach to Arakelov geometry, which doesnt require the variety under consideration to be generically smooth or projective. In order to construct such an approach we develop a theory of generalized
Deligne showed that every K3 surface over an algebraically closed field of positive characteristic admits a lift to characteristic 0. We show the same is true for a twisted K3 surface. To do this, we study the versal deformation spaces of twisted K3
We give an explicit weak solution to the Schottky problem, in the spirit of Riemann and Schottky. For any genus $g$, we write down a collection of polynomials in genus $g$ theta constants, such that their common zero locus contains the locus of Jacob
We treat Kollars injectivity theorem from the analytic (or differential geometric) viewpoint. More precisely, we give a curvature condition which implies Kollar type cohomology injectivity theorems. Our main theorem is formulated for a compact Kahler
We consider the rigid monoidal category of character sheaves on a smooth commutative group scheme $G$ over a finite field $k$ and expand the scope of the function-sheaf dictionary from connected commutative algebraic groups to this setting. We find t