arXiv subjects
Publications and source records attributed to Victor Hugo Jorge Pérez.
Let $(S,\mathfrak{m},k)$ and $(T,\mathfrak{n},k)$ be local rings, and let $R$ denote their fiber product over their common residue field $k$. Inspired by work of Naseh and Sather-Wagstaff, we explore consequences of vanishing of ${\rm Tor}^R_m(M,N)$ for various values of $m$, where $M$ and $N$ are finitely generated $R$-modules.
Let $\mathfrak{a}$ denote an ideal of a commutative Noetherian ring $R$. Let $M$ and $N$ be two $R$-modules. In this paper, we give partial answers on the extension of Hartshorne's conjecture about the cofiniteness of torsion and extension functors. For this purpose, we study the cofiniteness of the generalized local cohomology module $H^{i}_{\mathfrak{a}}(M, N)$ for a new class of modules, called $\mathfrak{a}$-weakly finite modules, in the local and non-local case. Furthermore, we derive some results on attached primes of top generalized local cohomology modules.