Related papers: An invariant for difference field extensions
In this paper we introduce a method of characteristic sets with respect to several term orderings for difference-differential polynomials. Using this technique, we obtain a method of computation of multivariate dimension polynomials of…
We introduce a new type of reduction of inversive difference polynomials that is associated with a partition of the basic set of automorphisms $\sigma$ and uses a generalization of the concept of effective order of a difference polynomial.…
In this paper, we introduce the commutativity degree of a finite-dimensional Lie algebra over a finite field and determine upper and lower bounds for it. Moreover, we study some relations between the notion of commutativity degree and known…
We introduce a notion of refinements in the context of patching, in order to obtain new results about local-global principles and field invariants in the context of quadratic forms and central simple algebras. The fields we consider are…
In this article, we study the generalized Poincare problem from the opposite perspective, by establishing lower bounds on the degree of the vector field in terms of invariants of the variety.
The defect of valued field extensions is a major obstacle in open problems in resolution of singularities and in the model theory of valued fields, whenever positive characteristic is involved. We continue the detailed study of defect…
We investigate distality and existence of distal expansions in valued fields and related structures. In particular, we characterize distality in a large class of ordered abelian groups, provide an AKE-style characterization for henselian…
Both a general and a diagonal u-invariant for forms of higher degree are defined, generalizing the u-invariant of quadratic forms. Both old and new results on these invariants are collected.
We develop a geometric theory for difference equations with a given group of automorphisms. To solve this problem we extend the class of difference fields to the class of absolutely flat simple difference rings called pseudofields. We prove…
The notion of degree begins in field theory as the dimension of a field extension. In algebraic geometry, this idea reappears as the degree of a finite morphism, defined using the induced extension of function fields. For proper morphisms…
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…
Recently, two first authors have introduced a group invariant, which is related to the number of elements $x$ and $y$ of a finite group $G$ such that $x\wedge y=1$ in the exterior square $G\wedge G$ of $G$. Research on this probability…
We construct new unbounded invariant distances on the universal cover of certain Legendrian isotopy classes. This is the first instance where unboundedness of an invariant distance is obtained without assuming the existence of a positive…
We describe differential invariants of infinite-dimensional algebras being equivalence algebras of some classes of PDE and study structure of these algebras.
We construct a new invariant metric for a compact subgroup of the automorphism group of a domain in complex space. Applications are provided.
The aim of this work is to offer a family of invariants that allows us to classify finite potent endomorphisms on arbitrary vector spaces, generalizing the classification of endomorphisms on finite-dimensional vector spaces. As a particular…
The hermitian u-invariants of a central simple algebra with involution are studied. In this context, a new technique is obtained to give bounds for the behavior of these invariants under a quadratic field extension. This is applied to…
We give an upper bound on the number of extensions of a fixed number field of prescribed degree and discriminant less than X; these bounds improve on work of Schmidt. We also prove various related results, such as lower bounds for the…
In this paper we propose and study a new structural invariant for graphs, called distance-unbalanced\-ness, as a measure of how much a graph is (un)balanced in terms of distances. Explicit formulas are presented for several classes of…
We consider an arbitrary representation of the additive group over a field of characteristic zero and give an explicit description of a finite separating set in the corresponding ring of invariants.