Can Yaylali - Derived $F$-zips

epiga:10375 - Épijournal de Géométrie Algébrique, 11 avril 2024, Volume 8 - https://doi.org/10.46298/epiga.2024.10375
Derived $F$-zipsArticle

Auteurs : 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
    Publié le : 11 avril 2024
    Accepté le : 21 novembre 2023
    Soumis le : 28 novembre 2022
    Mots-clés : Mathematics - Algebraic Geometry,14J10, 14F08, 14A30 (primary), 14F40, 14J28 (secondary)

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