Comparison of certain complexes of modules of generalized fractions and Cech complexes

Localization functors and cosupport in derived categories of commutative Noetherian rings

Let $R$ be a commutative Noetherian ring. We introduce the notion of localization functors $λ^W$ with cosupports in arbitrary subsets $W$ of $\text{Spec}\, R$; it is a common generalization of localizations with respect to multiplicatively closed subsets and left derived functors of ideal-adic completion functors. We prove several results about the localization functors $λ^W$, including an explicit way to calculate $λ^W$ by the notion of Cech complexes. As an application, we can give a simpler proof of a classical theorem by Gruson and Raynaud, which states that the projective dimension of a f…

多级通用初始理想、正则性以及d-Leray复形的最优彩色分数Helly定理

Multi-graded generic initial ideals, regularity, and the optimal colorful fractional Helly theorem for $d$-Leray complexes

该研究针对多级通用初始理想的正则性问题，基于特定单项式序证明了R/I正则性的下界，并将其应用得出d-Leray单纯复形的最优彩色分数Helly定理。