Geodesic
Derived $F$-zips
Épijournal de Géométrie Algébrique, Tome 8 (2024)

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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.
DOI : 10.46298/epiga.2024.10375
Classification : 14A30, 14F08, 14F40, 14J10, 14J28 
@article{10_46298_epiga_2024_10375,
     author = {Yaylali, Can},
     title = {Derived $F$-zips},
     journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
     publisher = {mathdoc},
     volume = {8},
     year = {2024},
     doi = {10.46298/epiga.2024.10375},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/epiga.2024.10375/}
}
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Yaylali, Can. Derived $F$-zips. Épijournal de Géométrie Algébrique, Tome 8 (2024). doi: 10.46298/epiga.2024.10375

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