Year: 2026
Type: preprint
Abstract: Inspired from the work of P. Scholze on the finiteness of \(\mathbf{F}_{p}\)-cohomology groups of proper rigid-analytic varieties over \(p\)-adic fields, Zavyalov recently introduced the notion of almost coherent rings, which plays a key role in the almost ring theory. In this paper, we characterize almost coherent rings in terms of almost flat modules and almost absolutely pure modules, integrating numerous classical results into almost mathematics. Besides, we show that every almost coherent $R$-module is not almost isomorphic to a coherent $R$-module, giving a negative answer to a question proposed in [14,B. Zavyalov, {\it Almost coherent modules and almost coherent sheaves}, Memoirs of the European Mathematical Society 19. Berlin: European Mathematical Society (EMS), 2025].
Source: arXiv (Cornell University)
Author: Zhang, Xiaolei
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7125164244
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