Building Data for Stacky Covers
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866909201192714240 |
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| author | Ahlqvist, Eric |
| author_facet | Ahlqvist, Eric |
| contents | We define stacky building data for stacky covers in the spirit of Pardini and give an equivalence of (2,1)-categories between the category of stacky covers and the category of stacky building data. We show that every stacky cover is a flat root stack in the sense of Olsson and Borne--Vistoli and give an intrinsic description of it as a root stack using stacky building data. When the base scheme S is defined over a field, we give a criterion for when a birational building datum comes from a tamely ramified cover for a finite abelian group scheme, generalizing a result of Biswas--Borne. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_10290 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Building Data for Stacky Covers Ahlqvist, Eric Algebraic Geometry Number Theory 14D20, 14D23, 14E20, 14E22, 19D23 We define stacky building data for stacky covers in the spirit of Pardini and give an equivalence of (2,1)-categories between the category of stacky covers and the category of stacky building data. We show that every stacky cover is a flat root stack in the sense of Olsson and Borne--Vistoli and give an intrinsic description of it as a root stack using stacky building data. When the base scheme S is defined over a field, we give a criterion for when a birational building datum comes from a tamely ramified cover for a finite abelian group scheme, generalizing a result of Biswas--Borne. |
| title | Building Data for Stacky Covers |
| topic | Algebraic Geometry Number Theory 14D20, 14D23, 14E20, 14E22, 19D23 |
| url | https://arxiv.org/abs/2012.10290 |