Work

Derived $F$-zips

Year: 2024

Type: article

Abstract: 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. Comment: 72 pages. Final version

Source: Épijournal de Géométrie Algébrique

DOI: 10.46298/epiga.2024.10375

Author: Can Yaylali

Institution: Technische Universität Darmstadt

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Deutsche Forschungsgemeinschaft

Award: TRR 326: Geometrie und Arithmetik uniformisierter Strukturen (GAUS)