Related papers: Generators for extensions of valuation rings

We give a short argument why the tensor product valuation on $K \otimes_k L$ is multiplicative when $k$ is an algebraically closed valued field and $K$ and $L$ are valued extensions (all valuations being in $\bR$). When the valuation on $k$…

Let G be an algebraic group defined over an algebraically closed field k of characteristic zero. We give a simple proof of the following result: if H^1(L, G) = {1} for some finitely generated field extension L/k of transcendence degree \ge…

Quadratic harnesses are time-inhomogeneous Markov polynomial processes with linear conditional expectations and quadratic conditional variances with respect to the past-future filtrations. Typically they are determined by five numerical…

Generators for the module of vector fields liftable over corank 1 stable complex analytic maps from an n-manifold to an (n+1)-manifold are found. This is applied to the classification of the singularities occuring in generic one-parameter…

Let $K=k((t))$ be a local field of characteristic $p>0$, with perfect residue field $k$. Let $\vec{a}=(a_0,a_1,\dots,a_{n-1})\in W_n(K)$ be a Witt vector of length $n$. Artin-Schreier-Witt theory associates to $\vec{a}$ a cyclic extension…

Rings of integer-valued polynomials are known to be atomic, non-factorial rings furnishing examples for both irreducible elements for which all powers factor uniquely (\emph{absolutely irreducibles}) and irreducible elements where some…

We prove the finite generation of canonical rings of projective variety of general type defined over complex numbers.

Motivated by the classical ideas of generating functions for orthogonal polynomials, we initiate a new line of investigation on "generating operators" for a family of differential operators between two manifolds. We prove a novel formula of…

The goal of this paper is to generalize and refine the classical ramification theory of complete discrete valuation rings to more general valuation rings, in the case of Artin-Schreier extensions. We define refined versions of invariants of…

Let $\mathscr{R}$ denote the ring of real polynomials on $\mathbb{R}^{n}$. Fix $m\geq 0$, and let $A_{1},\cdots ,A_{M}\in \mathscr{R}$. The $ C^{m}$-closure of $\left( A_{1},\cdots ,A_{M}\right) $, denoted here by $ \left[ A_{1},\cdots…

We prove that the cohomology ring of a finite-dimensional restricted Lie superalgebra over a field of characteristic $p > 2$ is a finitely-generated algebra. Our proof makes essential use of the explicit projective resolution of the trivial…

In this paper, we extend the theory of minimal limit key polynomials of valuations on the polynomial ring $\kx$. We use the theory of cuts on ordered abelian groups to show that the previous results on bounded sets of key polynomials of…

This paper explores the existence and distribution of primitive elements in finite field extensions with prescribed traces in several intermediate field extensions. Our main result provides an inequality-like condition to ensure the…

Let $L$ be the language of rings. We provide an axiomatization of the $L$-theories of quaternions and octonions and characterize their models: they coincide, up to isomorphism, with quaternion and octonion algebras over a real closed field,…

In the algebraic theory of K-stability, one of the most challenging problems is to show the graded algebra associated with certain higher rank quasi-monomial valuations are finitely generated. In the global case of Fano varieties and local…

We deal with two forms of the "uniqueness cases" in the classification of large simple $K^*$-groups of finite Morley rank of odd type, where large means the $m_2(G)$ at least three. This substantially extends results known for even larger…

In a recent article a generalization of the binomial distribution associated with a sequence of positive numbers was examined. The analysis of the nonnegativeness of the formal expressions was a key-point to allow to give them a statistical…

For an odd prime p, we determine a minimal set of topological generators of the pro-p Iwahori subgroup of a split reductive group G over Z\_p. In the simple adjoint case and for any sufficiently large regular prime p, we also construct…

Let $F=\mathbb{F}_q(T)$ be the field of rational functions with $\mathbb{F}_q$-coefficients, and $A=\mathbb{F}_q[T]$ be the subring of polynomials. Let $D$ be a division quaternion algebra over $F$ which is split at $1/T$. Given an…

Let $K$ be a field, let $\sigma$ be an automorphism of $K$, and let $\delta$ be a derivation of $K$. We show that if $D$ is one of $K(x;\sigma)$ or $K(x;\delta)$, then $D$ either contains a free algebra over its center on two generators, or…