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arXiv · 2208.00869

Flat relative Mittag-Leffler modules and Zariski locality

Asmae Ben Yassine·Jan Trlifaj
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Abstract

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.

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Asmae Ben Yassine, Jan Trlifaj. 2022-08-01. Flat relative Mittag-Leffler modules and Zariski locality. https://doi.org/10.1016/j.jpaa.2024.107834

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