Ext, Tor and the Uct
نویسنده
چکیده
منابع مشابه
On natural homomorphisms of local cohomology modules
Let $M$ be a non-zero finitely generated module over a commutative Noetherian local ring $(R,mathfrak{m})$ with $dim_R(M)=t$. Let $I$ be an ideal of $R$ with $grade(I,M)=c$. In this article we will investigate several natural homomorphisms of local cohomology modules. The main purpose of this article is to investigate when the natural homomorphisms $gamma: Tor^{R}_c(k,H^c_I(M))to kotim...
متن کاملNote on regular and coregular sequences
Let R be a commutative Noetherian ring and let M be a nitely generated R-module. If I is an ideal of R generated by M-regular sequence, then we study the vanishing of the rst Tor functors. Moreover, for Artinian modules and coregular sequences we examine the vanishing of the rst Ext functors.
متن کاملNotes on Tor and Ext
1. Basic homological algebra 1 1.1. Chain complexes 2 1.2. Maps and homotopies of maps of chain complexes 2 1.3. Tensor products of chain complexes 3 1.4. Short and long exact sequences 3 1.5. Dual cochain complexes and Hom complexes 4 1.6. Relations between ⊗ and Hom 4 2. The universal coefficient and Künneth theorems 5 2.1. Universal coefficients in homology 5 2.2. The Künneth theorem 6 2.3. ...
متن کاملAsymptotic Behavior of Tor over Complete Intersections and Applications
Let R be a local complete intersection and M,N are R-modules such that l(Tor i (M,N)) < ∞ for i ≫ 0. Imitating an approach by Avramov and Buchweitz, we investigate the asymptotic behavior of l(Tor i (M,N)) using Eisenbud operators and show that they have well-behaved growth. We define and study a function η(M,N) which generalizes Serre’s intersection multiplicity χ(M,N) over regular local rings...
متن کاملSome applications of Gröbner bases in homological algebra
In this paper we make some computations in homological algebra using Gröbner bases for modules over polynomials rings with coefficients in a Noetherian commutative ring. In particular, we show easy procedures for computing the Ext and Tor modules.
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تاریخ انتشار 2012