Related papers: The defect formula
In this paper, we undertake a systematic model and valuation theoretic study of the class of ordered fields which are dense in their real closure. We apply this study to determine definable henselian valuations on ordered fields, in the…
Given a right eigenvector $x$ and a left eigenvector $y$ associated with the same eigenvalue of a matrix $A$, there is a Hermitian positive definite matrix $H$ for which $y=Hx$. The matrix $H$ defines an inner product and consequently also…
In order to develop a differential calculus for error propagation we study local Dirichlet forms on probability spaces with square field operator $\Gamma$ -- i.e. error structures -- and we are looking for an object related to $\Gamma$…
Consider a smooth affine algebraic variety $X$ over an algebraically closed field, and let a finite group $G$ act on it. We assume that the characteristic of the field is greater than the dimension of $X$ and the order of $G$. An explicit…
This paper discusses the notion of a deformation quantization for an arbitrary polynomial Poisson algebra A. We examine the Hochschild cohomology group H^3(A) and find that if a deformation of A exists it can be given by bidifferential…
Suppose that (K, $\nu$) is a valued field, f (z) $\in$ K[z] is a unitary and irreducible polynomial and (L, $\omega$) is an extension of valued fields, where L = K[z]/(f (z)). Further suppose that A is a local domain with quotient field K…
We investigate the Hasse principles for isotropy and isometry of quadratic forms over finitely generated field extensions with respect to various sets of discrete valuations. Over purely transcendental field extensions of fields that…
We prove in arbitrary characteristic that an immediate valued algebraic function field $F$ of transcendence degree 1 over a tame field $K$ is contained in the henselization of $K(x)$ for a suitably chosen $x\in F$. This eliminates…
Using the ramification theory of tame and Kaplansky fields, we show that maximal Kaplansky fields contain maximal immediate extensions of each of their subfields. Likewise, algebraically maximal Kaplansky fields contain maximal immediate…
We show that an algebraic immediate valuation ring extension of characteristic $p>0$ is a filtered union of complete intersection algebras of finite type.
A henselian valued field $K$ is called a tame field if its algebraic closure $\tilde{K}$ is a tame extension, that is, the ramification field of the normal extension $\tilde{K}|K$ is algebraically closed. Every algebraically maximal…
This paper is concerned with algebraic geometry over complete discretely valued fields $K$ of equicharacteristic zero. Several results are given including: the canonical projection $K^{n} \times K\mathbb{P}^{m} \longrightarrow K^{n}$ and…
Over a field of characteristic $0$ we give a concrete, computation--ready description of Jordan algebra structures and their low--order deformation theory. The Jordan identity is quartic in the elements and cubic in the multiplication, and…
We give a characterization, in terms of the residue field, of those henselian valuation rings and those henselian valuation ideals that are diophantine. This characterization gives a common generalization of all the positive and negative…
Two well studied invariants of a complex projective variety are the unit Euclidean distance degree and the generic Euclidean distance degree. These numbers give a measure of the algebraic complexity for "nearest" point problems of the…
Let $K$ be a normal subgroup of the finite group $H$. To a block of a $K$-interior $H$-algebra we associate a group extension, and we prove that this extension is isomorphic to an extension associated to a block given by the Brauer…
We derive a formula expanding the bracket with respect to a natural deformation parameter. The expansion is in terms of a two-variable polynomial algebra of diagram resolutions generated by basic operations involving the Goldman bracket. A…
This article is a natural construction of our previous works. In this article, we employ similar ideas due to MacLane to provide an estimate of IC(K(X)|K,v) when (K(X)|K,v) is a valuation algebraic extension. Our central result is an…
We introduce a notion of valued module which is suitable to study valued fields of positive characteristic. Then we built-up a robust theory of henselianity in the language of valued modules and prove Ax-Kochen Ershov type results.
We present a geometrical framework which incorporates higher derivative corrections to the action of N = 2 vector multiplets in terms of an enlarged scalar manifold which includes a complex deformation parameter. This enlarged space carries…