Related papers: On Faltings' annihilator theorem

Let $\mathfrak{q}$ be an ideal of a Noetherian local ring $(A,\mathfrak{m})$ and $M$ a non-zero finitely generated $A$-module. We present a criterion of Cohen-Macaulayness of the form module $G_M(\mathfrak{q})$ in terms of (non-)vanishing…

In a recent paper [El 13], M.E. Kahoui has shown that if $R$ is a polynomial ring over $\mathbb{C}$, $A$ an $\mathbb{A}^3$-fibration over $R$, and $W$ a residual variable of $A$ then $A$ is stably polynomial over $R[W]$. In this article we…

Let $(R,\my)$ be a noetherian local ring and let $M$ be an $R$-module such that $\bigcap\limits_{n\geq 1} \my^n M=0.$ Let $\hat{M}$ be the completion of $M$. We show that Ass$(\hat{M})=$ Koatt$(M)$ holds in the following three cases: if…

We prove a mixed-characteristic analogue of Kunz's theorem in terms of perfectoid towers: a Noetherian local ring of residue characteristic $p$ is regular if and only if it admits a flat map to a Noetherian ring that extends to a perfectoid…

Let $f:X\rightarrow Y$ be a K\"{a}hler fibration from a complex manifold $X$ to an analytic space $Y$. We show several relative Nadel-type vanishing theorems.

In this article we prove that for a basic classical Lie superalgebra the annihilator of a strongly typical Verma module is a centrally generated ideal. For a basic classical Lie superalgebra of type I we prove that the localization of the…

We introduce a notion of inertial equivalence for integral $\ell$-adic representation of the Galois group of a global field. We show that the collection of continuous, semisimple, pure $\ell$-adic representations of the absolute Galois…

We show that if Auslander`s depth formula holds for non-zero Tor-independent modules over Cohen-Macaulay local rings of dimension 1, then it holds for such modules over any Cohen-Macaulay local ring. More generally, we show that the depth…

A 2003 counterexample to a conjecture of Auslander brought attention to a family of rings - colloquially called AC rings - that satisfy a natural condition on vanishing of cohomology. Several results attest to the remarkable homological…

Parkash and Kour obtained a new version of Cohen's theorem for Noetherian modules, which states that a finitely generated $R$-module $M$ is Noetherian if and only if for every prime ideal $\mathfrak{p}$ of $R$ with Ann$(M)\subseteq…

Let $k$ be an uncountable algebraically closed field and let $A$ be a countably generated left Noetherian $k$-algebra. Then we show that $A \otimes_k K$ is left Noetherian for any field extension $K$ of $k$. We conclude that all subfields…

Let $R$ be a commutative Noetherian ring, $\fa$ an ideal of $R$, $M$ an arbitrary $R$-module and $N$ a finite $R$-module. We prove that \cite[Theorem 2.1]{Mel} and \cite[Proposition 3.3 (i)$\Leftrightarrow$(ii)]{B1} are true for any Serre…

The purpose of this paper is to study finiteness conditions on injective hulls of simple modules over Noetherian Down-Up algebras. We will show that the Noetherian Down-Up algebras A(\alpha,\beta,\gamma) which are fully bounded are…

Let $R$ be a commutative Noetherian ring with identity (not necessarily local) and $\frak a$ a proper ideal of $R$. We study the invariance of some classes of $\frak a$-relative Cohen-Macaulay modules under pure ring homomorphisms and ring…

In this paper, we partially complete the local Rankin-Selberg theory of Asai $L$-functions and $\epsilon$-factors as introduced by Flicker and Kable. In particular, we establish the relevant local functional equation at Archimedean places…

Let R be a commutative Noetherian ring of prime characteristic and M be an x-divisible right R[x,f]-module that is Noetherian as R-module. We give an affirmative answer to the question of Sharp and Yoshino in the case where R is semi-local…

We establish connections between the concepts of Noetherian, regular coherent, and regular n-coherent categories for Z-linear categories with finitely many objects and the corresponding notions for unital rings. These connections enable us…

Let $\fa$ be an ideal of a Noetherian local ring $(R,\fm)$ and $M$ a finitely generated $R$-module. In this paper we introduce some criterions on Artinianness of formal local cohomology, in particular vanishing and finiteness of local…

We explore the singularity classes $F$-nilpotent, weakly $F$-nilpotent, and generalized weakly $F$-nilpotent under faithfully flat local ring maps. As an application, we show that the loci of primes in a Noetherian ring of prime…

We prove that a classical theorem of McAdam about the analytic spread of an ideal in a Noetherian local ring is true for divisorial filtrations on an excellent local ring $R$ which is either of equicharacteristic zero or of dimension $\le…