Can Yaylali - Derived $F$-zips

epiga:10375 - Épijournal de Géométrie Algébrique, April 11, 2024, Volume 8 -
Derived $F$-zipsArticle

Authors: Can Yaylali

    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.

    Volume: Volume 8
    Published on: April 11, 2024
    Accepted on: November 21, 2023
    Submitted on: November 28, 2022
    Keywords: Mathematics - Algebraic Geometry,14J10, 14F08, 14A30 (primary), 14F40, 14J28 (secondary)

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