Related papers: Stable trace ideals and applications

This paper extends the trace formulas of [5] with perturbations in normed ideals of $B(H)$ to multivariate functions of commuting contractions admitting a dilation to commuting normal contractions.

Given an homogeneous monomial ideal $I$, we provide a question- and example-based investigation of the stabilization patterns of the Betti tables shapes of $I^d$ as we vary $d$. We build off Whieldon's definition of the stabilization index…

Let $R=K[x_1,\ldots, x_n]$ be the polynomial ring in $n$ variables over a field $K$ and $I$ be monomial ideal of $R$. In this paper, we show that if $I$ is a generic monomial ideal, then $R/I$ is pretty clean if and only if $R/I$ is…

We construct bounded, commuting projections for the three-dimensional de Rham complex with the additional property that the projections preserve the trace of functions/fields if the latter is a piecewise polynomial in the appropriate trace…

Let $A$ be a direct limit of a direct system of Cohen-Macaulay rings. In this paper, we describe the Cohen-Macaulay property of $A$. Our results indicate that $A$ is not necessarily Cohen-Macaulay. We show $A$ is Cohen-Macaulay under…

In two dimensional regular local rings integrally closed ideals have a unique factorization property and have a Cohen-Macaulay associated graded ring. In higher dimension these properties do not hold for general integrally closed ideals and…

We prove that sequentially Cohen-Macaulay rings in positive characteristic, as well as sequentially Cohen-Macaulay Stanley-Reisner rings in any characteristic, have trivial Lyubeznik table. Some other configurations of Lyubeznik tables are…

We find analytical solutions to the Cahn-Hilliard equation for the dynamics of an interface in a system with a conserved order parameter (Model B). We show that, although steady-state solutions of Model B are unphysical in the far-field,…

A commutative ring $R$ is stable if every non-zero ideal $I$ of $R$ is projective over its ring of endomorphisms. Motivated by a paper of Bass in the 1960s, stable rings have received wide attention in the literature ever since then. Much…

We examine virtual resolutions of Stanley-Reisner ideals for a product of projective spaces. In particular, we provide sufficient conditions for a simplicial complex to be virtually Cohen-Macaulay (to have a virtual resolution with length…

We study the K'-theory of a CM Henselian local ring R of finite Cohen-Macaulay type. We first describe a long exact sequence involving the groups $K_i'(R)$ and the K-groups of certain other rings, including the Auslander algebra. By…

In this work we describe a minimal log-resolution of an ideal in a smooth complex surface from the minimal log-resolution of its generators.

In this paper we provide a detailed topological and measure-theoretic study of Lebesgue measure-preserving circle maps that are rotated with inner and outer rotations which are independent of each other. In particular, we analyze the…

This is one of a series of articles, in collaboration with C. Moeglin, whose goal is to stabilize the twisted trace formula. In the previous article, we have stated several assertions about the stabilization of weighted orbital integrals…

Explicit examples of {\bf positive} crystalline measures and Fourier quasicrystals are constructed using pairs of stable of polynomials, answering several open questions in the area.

We model the phase oscillations of electrons in race-track microtrons by means of an area preserving map with a fixed point at the origin, which represents the synchronous trajectory of a reference particle in the beam. We study the…

Inspired by the works in linkage theory of ideals, we define the concept of linkage of ideals over a module. Several known theorems in linkage theory are improved or recovered by new approaches. Specially, we make some extensions and…

Let F be a number field and $\widetilde{\mathrm{Sp}}(2n)$ be the metaplectic covering of Weil of $\mathrm{Sp}(2n, \mathbb{A}_F)$. We stabilize the elliptic semi-simple terms of the genuine part of trace formula for…

In this paper, we introduce and study the notion of linkage by perfect modules, which we call perfect linkage, for Cohen-Macaulay modules over Cohen--Macaulay local rings. We explore perfect linkage in connection with syzygies, maximal…

We construct two examples of invariant manifolds that despite being locally unstable at every point in the transverse direction are globally stable. Using numerical simulations we show that these invariant manifolds temporarily repel nearby…