Flat relative Mittag-Leffler modules and Zariski locality
| Autor: | Yassine, Asmae Ben, Trlifaj, Jan |
|---|---|
| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: Revised version, extending the main results of v1 from classes of finite type to definable closures of Tor-orthogonal classes. The latter have more applications, e.g., to n-Drinfeld vector bundles |
| Databáze: | arXiv |
| Externí odkaz: |
|