Related papers: Closure operations in complete local rings of mixe…

We study the behaviour of the finiteness of the set of associated primes of local cohomology modules, more generally of Lyubeznik functors, under various ring extensions. At first, we review the results for flat and faithfully flat…

Let $p$ be a prime. Let $V$ be a discrete valuation ring of mixed characteristic $(0,p)$ and index of ramification $e$. Let $f: G \rightarrow H$ be a homomorphism of finite flat commutative group schemes of $p$ power order over $V$ whose…

We prove that the absolute integral closure $R^{+}$ of an equicharacteristic zero noetherian complete local domain $R$ is not coherent, provided $\dim(R)\geq 2$. As a corollary, we give an elementary proof of the mixed characteristic…

We develop a formalism of unit $F$-modules in the style of Lyubeznik and Emerton-Kisin for rings which have finite $F$-representation type after localization and completion at every prime ideal. As applications, we show that if $R$ is such…

The aim of this article is to prove some results on the existence of an integral extension domain of a complete local Noetherian domain in mixed characteristic $p>0$ having certain distinguished properties with respect to the Frobenius map.…

In this paper we give a characterisation of real closure * of regular rings, which is quite similar to the characterisation of real closure * of Baer regular rings seen in [4]. We also characterize Baer-ness of regular rings using near-open…

Let $R\subset F$ be an extension of real closed fields and ${\mathcal S}(M,R)$ the ring of (continuous) semialgebraic functions on a semialgebraic set $M\subset R^n$. We prove that every $R$-homomorphism $\varphi:{\mathcal S}(M,R)\to F$ is…

Internal preneighbourhood spaces inside any finitely complete category with finite coproducts and proper factorisation structure were first introduced in my earlier paper. This paper proposes a closure operation on internal preneighbourhood…

This paper establishes uniform bounds in characteristic $p$ rings which are either F-finite or essentially of finite type over an excellent local ring. These uniform bounds are then used to show that the Hilbert-Kunz length functions and…

We give sufficient conditions which ensure that a functor of finite length from an additive category to finite-dimensional vector spaces has a projective resolution whose terms are finitely generated. For polynomial functors, we study also…

We prove that the class of all loops with the inverse property (IP loops) has the Finite Embedding Property (FEP). As a consequence, every group is locally embeddable into finite IP loops.

Let $R$ be an excellent Noetherian ring of prime characteristic. Consider an arbitrary nested pair of ideals (or more generally, a nested pair of submodules of a fixed finite module). We do \emph{not} assume that their quotient has finite…

Given an algebraic function field $F|K$ and a place $\wp$ on $K$, we prove that the places that are composite with extensions of $\wp$ to finite extensions of $K$ lie dense in the space of all places of $F$, in a strong sense. We apply the…

Let $K$ be a field of characteristic 0 and $S=K[x_1,\ldots,x_m]/I$ be an affine domain. Consider $R=S_P$ where $P\in Spec(S)$ such that $R$ is regular. In this paper we construct a field $F$ which is contained in $R$ such that (1) The…

We study the long-term behavior of the iteration of a random map consisting of Lipschitz transformations on a compact metric space, independently and randomly selected according to a fixed probability measure. Such a random map is said to…

Using a result of M. Hochster and C. Huneke on $F$-rational rings a criterion for complete intersection rings of characteristic $p>0$ is presented. As an application, we give a completely different proof for an algebraic result of G.…

The spectral envelope S(F) of a subset of integers is the set of probability measures on the circle group that are weak star limits of squared moduli of trigonometric polynomials with frequencies in F. Fourier transforms of these measures…

The intent of this paper is to present a set of axioms that are sufficient for a closure operation to generate a balanced big Cohen-Macaulay module B over a complete local domain R. Conversely, we show that if such a B exists over R, then…

Let $\Omega$ be a bounded domain with convex boundary in a complete noncompact Riemannian manifold with Bakry-\'Emery Ricci curvature bounded below by a positive constant. We prove a lower bound of the first eigenvalue of the weighted…

The present work is devoted to an extension of the well-known Ehrling inequalities, which quantitatively characterize compact embeddings of function spaces, to more general operators. Firstly, a modified notion of continuity for linear…