Derived $F$-zips
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866914603069341696 |
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| author | Yaylali, Can |
| author_facet | Yaylali, Can |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_01517 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Derived $F$-zips Yaylali, Can Algebraic Geometry 14J10, 14F08, 14A30 (primary), 14F40, 14J28 (secondary) 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. |
| title | Derived $F$-zips |
| topic | Algebraic Geometry 14J10, 14F08, 14A30 (primary), 14F40, 14J28 (secondary) |
| url | https://arxiv.org/abs/2208.01517 |