Related papers: Filtered colimits of complete intersection algebra…
T. Saito established a ramification theory for ring extensions locally of complete intersection. We show that for a Henselian valuation ring $A$ with field of fractions $K$ and for a finite Galois extension $L$ of $K$, the integral closure…
The category of Hilbert spaces and contractions has filtered colimits, and tensoring preserves them. We also discuss (problems with) bounded maps.
It is a fairly known fact that most of the algebras appearing in the theory of rings of differential operators, quantized algebras of different kinds (including many quantum groups), regular algebras in projective non-commutative geometry,…
Fix a prime number $p$. We report on some recent developments in algebraic geometry (broadly construed) over $p$-adically complete commutative rings. These developments include foundational advances within the subject as well as external…
We associate to any given finite set of valuations on the polynomial ring in two variables over an algebraically closed field a numerical invariant whose positivity characterizes the case when the intersection of their valuation rings has…
In this exposition we discuss the theory of algebraic extensions of valued fields. Our approach is mostly through Galois theory. Most of the results are well-known, but some are new. No previous knowledge on the theory of valuations is…
We consider complete intersection ideals in a polynomial ring over a field of characteristic zero that are stable under the action of the symmetric group permuting the variables. We determine the possible representation types for these…
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 give a purely scheme theoretic construction of the filtration by ramification groups of the Galois group of a covering. The valuation need not be discrete but the normalizations are required to be locally of complete intersection.
In this note we relate the valuations of the algebras appearing in the non-commutative geometry of quantized algebras to properties of sub-lattices in some vector spaces. We consider the case of algebras with $PBW$-bases and prove that…
We study the problem of the existence of filtered multiplicative bases of a restricted enveloping algebra u(L), where L is a finite-dimensional and p-nilpotent restricted Lie algebra over a field of positive characteristic p.
This note gathers what is known about, and provides some new results concerning the operations of intersection, of ``generated $\sigma$-field'', and of ``complementation'' for (independent) complete $\sigma$-fields on probability spaces.
We present a general framework in the setting of difference ring extensions that enables one to find improved representations of indefinite nested sums such that the arising denominators within the summands have reduced degrees. The…
Consider a simple algebraic valued field extension $(L/K,v)$ and denote by $\mathcal O_L$ and $\mathcal O_K$ the corresponding valuation rings. The main goal of this paper is to present, under certain assumptions, a description of $\mathcal…
In this paper we give conditions on a homogeneous polynomial for which the associated graded Artin algebra is a complete intersection.
Let $\mathcal{R}$ be a finite valuation ring of order $q^r$. In this paper we generalize and improve several well-known results, which were studied over finite fields $\mathbb{F}_q$ and finite cyclic rings $\mathbb{Z}/p^r\mathbb{Z}$, in the…
Interval graphs are intersection graphs of closed intervals. A generalization of recognition called partial representation extension was introduced recently. The input gives an interval graph with a partial representation specifying some…
Let $A$ be a commutative noetherian ring and $I$ an ideal in $A$. We characterize algebraically when all the minimal primes of the associated graded ring $G_I A$ contract to minimal primes of $A/I$. This, applied to intersection theory,…
We introduce a notion of strict complete intersections with respect to Cox rings and we prove Galois descent for this new notion.
We give a simplified complete proof for the classification of the selfinjective representation-finite algebras of finite dimension over an algebraically closed field. We explain the relations between the two different approaches and also to…