Torsion pairs in categories of modules on ringed finite sites

2024/03/22 by Wu, Mawei
#13D30 #16S90 #18A25 #18E05 #18F20 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2403.15001

Abstract

Let C be a small category. In this paper, we mainly study the category of modules \mathfrakMod-\mathfrakR on ringed sites (C,\mathfrakR). We firstly reprove the Theorem A of the paper (M. Wu and F. Xu. Skew category algebras and modules on ringed finite sites. J. A. 631, 2023), then we characterize \mathfrakMod-\mathfrakR in terms of the torsion modules on Gr(\mathfrakR), where Gr(\mathfrakR) is the linear Grothendieck construction of \mathfrakR. Finally, we investigate the hereditary torsion pairs, TTF triples and Abelian recollements of \mathfrakMod-\mathfrakR. When C is finite, the complete classifications of all these are given respectively.

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