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| Main Authors: | , |
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| Format: | Preprint |
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2022
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| Online Access: | https://arxiv.org/abs/2208.00869 |
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| _version_ | 1866913806089715712 |
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| author | Yassine, Asmae Ben Trlifaj, Jan |
| author_facet | Yassine, Asmae Ben Trlifaj, Jan |
| contents | The ascent and descent of the Mittag-Leffler property were instrumental in proving Zariski locality of the notion of an (infinite dimensional) vector bundle by Raynaud and Gruson in \cite{RG}. More recently, relative Mittag-Leffler modules were employed in the theory of (infinitely generated) tilting modules and the associated quasi-coherent sheaves, \cite{AH}, \cite{HST}. Here, we study the ascent and descent along flat and faithfully flat homomorphisms for relative versions of the Mittag-Leffler property. In particular, we prove the Zariski locality of the notion of a locally f-projective quasi-coherent sheaf for all schemes, and for each $n \geq 1$, of the notion of an $n$-Drinfeld vector bundle for all locally noetherian schemes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_00869 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Flat relative Mittag-Leffler modules and Zariski locality Yassine, Asmae Ben Trlifaj, Jan Algebraic Geometry Commutative Algebra 13D07 The ascent and descent of the Mittag-Leffler property were instrumental in proving Zariski locality of the notion of an (infinite dimensional) vector bundle by Raynaud and Gruson in \cite{RG}. More recently, relative Mittag-Leffler modules were employed in the theory of (infinitely generated) tilting modules and the associated quasi-coherent sheaves, \cite{AH}, \cite{HST}. Here, we study the ascent and descent along flat and faithfully flat homomorphisms for relative versions of the Mittag-Leffler property. In particular, we prove the Zariski locality of the notion of a locally f-projective quasi-coherent sheaf for all schemes, and for each $n \geq 1$, of the notion of an $n$-Drinfeld vector bundle for all locally noetherian schemes. |
| title | Flat relative Mittag-Leffler modules and Zariski locality |
| topic | Algebraic Geometry Commutative Algebra 13D07 |
| url | https://arxiv.org/abs/2208.00869 |