相关论文: Lemme d'Artin-Rees, theoreme d'Izumi et fonction d…

We express multiplicities and degree functions of graded families of $\mathfrak{m}_R$-primary ideals in an excellent normal local ring $(R,\mathfrak{m}_R)$ as limits of intersection products. Moreover, in dimension 2, we show more refined…

We use the properties of Hermite and Kamp\'e de F\'eriet polynomials to get closed forms for the repeated derivatives of functions whose argument is a quadratic or higher-order polynomial. The results we obtain are extended to product of…

For a standard graded algebra $R$, we consider embeddings of the the poset of Hilbert functions of quotients of $R$ into the poset of ideals of $R$, as a way of classification of Hilbert functions. There are examples of rings for which such…

Through a cascade of generalizations, we develop a theory of motivic integration which works uniformly in all non-archimedean local fields of characteristic zero, overcoming some of the difficulties related to ramification and small residue…

We introduce the notion of relation type of an affine algebra and prove that it is well defined by using the Jacobi-Zariski exact sequence of Andr\'e-Quillen homology. In particular, the relation type is an invariant of an affine algebraic…

Consider the representations of an algebraic group G. In general, polynomial invariant functions may fail to separate orbits. The invariant subring may not be finitely generated, or the number and complexity of the generators may grow…

Our main theorem is that the word problem in the Artin group G = <a,b,c | aba=bab, ac=ca, {}_{n}(b,c) = {}_{n}(c,b) > for n >= 5 can be solved using a system R of length preserving rewrite rules that, together with free reduction, can be…

We show that the sum of the traces of Frobenius elements of Artin $L$-functions in a family of $G$-fields satisfies the Gaussian distribution under certain counting conjectures. We prove the counting conjectures for $S_4$ and $S_5$-fields.…

Let $J\subset I$ be ideals in a formally equidimensional local ring with $\lambda(I/J)<\infty.$ Rees proved that for all $n\gg0$, $\lambda(I^n/J^n)$ is a polynomial $P(I/J)(X)$ in $n$ of degree at most dim $R$ and $J$ is a reduction of $I$…

We derive integral representations for the Rankin-Selberg L-functions on GL(3) x GL(1) and GL(3) x GL(2) by a process of unipotent averaging at archimedean places. A key feature of our result is that it allows one to fix the choice of test…

We focus on a branch of region-based spatial logics dealing with affine geometry. The research on this topic is scarce: only a handful of papers investigate such systems, mostly in the case of the real plane. Our long-term goal is to…

This paper presents a general study of one-dimensional differentiability for functionals defined on convex domains that are not necessarily open. The local approximation is carried out using affine functionals, as opposed to linear…

We prove a function-field analogue of Bourgain's $L^2$ pointwise ergodic theorem. Let $q$ be a power of a prime $p$, let $\mathbb{F}_q[t]$ be the ring of polynomials over the finite field $\mathbb{F}_q$, and let $\mathbb{F}_q[t][u]$ be the…

Suppose L is any finite algebraic extension of either the ordinary rational numbers or the p-adic rational numbers. Also let g_1,...,g_k be polynomials in n variables, with coefficients in L, such that the total number of monomial terms…

We establish the existence of a finite-dimensional unitary realization for every matrix-valued rational inner function from the Schur--Agler class on a unit square-matrix polyball. In the scalar-valued case, we characterize the denominators…

Let $\mathcal{P}$ be a property of function $\mathbb{F}_p^n \to \{0,1\}$ for a fixed prime $p$. An algorithm is called a tester for $\mathcal{P}$ if, given a query access to the input function $f$, with high probability, it accepts when $f$…

The notion of a root functional of a system of polynomials or ideal of polynomials is a generalization of the notion of a root, in particular, for a multiple root. A root functional is a linear functional that is defined on a polynomial…

We construct "pushing maps" on the cube complexes that model right-angled Artin groups (RAAGs) in order to study filling problems in certain subsets of these cube complexes. We use radial pushing to obtain upper bounds on higher divergence…

We introduce a notion of integration defined from filters over families of finite sets. This procedure corresponds to determining the average value of functions whose range lies in any algebraic structure in which finite averages make…

We give a survey on the theory of representation-finite and certain minimal representation-infinite algebras.The main goals are the existence of multiplicative bases and of coverings with good properties. Both are attained via…