Mittag-Leffler modules and variants on intersection flatness
Abstract
We systematically study the intersection flatness and Ohm-Rush properties for modules over a commutative ring, drawing inspiration from the work of Ohm and Rush and of Hochster and Jeffries. We establish new structural results for modules that are intersection flat/Ohm-Rush by exhibiting intimate connections between these notions and the seminal work of Raynaud and Gruson on Mittag-Leffler modules. In particular, we develop a theory of Ohm-Rush modules that is parallel to the theory of Mittag-Leffler modules. We also obtain descent and local-to-global results for intersection flat/Ohm-Rush modules. Our investigations reveal a particularly pleasing picture for flat modules over a complete local ring, in which case many otherwise distinct properties coincide.
Cite
@article{arxiv.2305.11139,
title = {Mittag-Leffler modules and variants on intersection flatness},
author = {Rankeya Datta and Neil Epstein and Kevin Tucker},
journal= {arXiv preprint arXiv:2305.11139},
year = {2025}
}
Comments
Substantial revision and reduction in length, including a title change. Removed prime characteristic applications, which will appear in forthcoming work