2022/08/02 by Can Yaylali
Engineering · Computer Science · #math.AG
paper · pdf · doi:10.46298/epiga.2024.10375
We define derived versions of F-zips and associate a derived F-zip to any proper, smooth morphism of schemes in positive characteristic. We analyze the stack of derived F-zips and certain substacks. We make a connection to the classical theory and look at problems that arise when trying to generalize the theory to derived G-zips and derived F-zips associated to lci morphisms. As an application, we look at Enriques-surfaces and analyze the geometry of the moduli stack of Enriques-surfaces via the associated derived F-zips. As there are Enriques-surfaces in characteristic 2 with non-degenerate Hodge-de Rham spectral sequence, this gives a new approach, which could previously not be obtained by the classical theory of F-zips.