Related papers: Finite morphisms and Nash multiplicity sequences
The aim of this article is to find appropriate definitions for shifts of finite type and sofic shifts in a general context of symbolic dynamics. We start showing that the classical definitions of shifts of finite type and sofic shifts, as…
In this paper, we give a survey of the known results concerning the tensor rank of the multiplication in finite extensions of finite fields, enriched with some not published recent results as well as analyzes enhancing the qualitative…
We construct canonical heights of subvarieties for dynamical system of several morphisms associated with line bundles defined over a number field, and study some of their properties. We also construct invariant currents for such systems…
In this paper I survey some recent results on finite determination, convergence, and approximation of formal mappings between real submanifolds in complex spaces. A number of conjectures are also given.
A Nash group is said to be almost linear if it has a Nash representation with finite kernel. Structures and basic properties of these groups are studied.
We study centrality of morphisms in a setting derived from that of a pointed category in which binary products commute with coequalisers. The main results of this paper show that much of the behaviour of central morphisms for unital…
In the course of classifying the homogeneous permutations, Cameron introduced the viewpoint of permutations as structures in a language of two linear orders, and this structural viewpoint is taken up here. The majority of this thesis is…
Flexible mechanical metamaterials possess repeating structural motifs that imbue them with novel, exciting properties including programmability, anomalous elastic moduli and nonlinear and robust response. We address such structures via…
We study the arithmetical ranks and the cohomological dimensions of an infinite class of Cohen-Macaulay varieties of minimal degree. Among these we find, on the one hand, infinitely many set-theoretic complete intersections, on the other…
We define what we call morphisms of Cartan connections. We generalize the main theorems on Cartan connections to theorems on morphisms. Many of the known constructions involving Cartan connections turn out to be examples of morphisms. We…
This paper is a review containing new original results on the finite order variational sequence and its different representations with emphasis on applications in the theory of variational symmetries and conservation laws in physics.
In this paper, we study some topological characteristics of the n-normed spaces. We observe convergence sequences, closed sets, and bounded sets in the n-normed spaces using norms of quotient spaces that will be constructed. These norms…
We study analogues of Tate's conjecture on homomorphisms for abelian varieties when the ground field is finitely generated over an algebraic closure of a finite field. Our results cover the case of abelian varieties without nontrivial…
Finite topological spaces are in bijective correspondence with preorders on finite sets. We undertake their study using combinatorial tools that have been developed to investigate general discrete structures. A particular emphasis will be…
This is a survey paper dealing with moduli aspects of curves over finite fields. It discusses counting points of moduli spaces, relations with modular forms and stratifications on moduli spaces.
In a category $\mathcal{C}$ with a proper $(\mathcal{E}, \mathcal{M})$-factorization system, we study the notions of strict, co-strict, initial and final morphisms with respect to a topogenous order. Besides showing that they allow…
We study sampling and interpolation arrays with multiplicities for the spaces P_k of holomorphic polynomials of degree at most k. We find that the geometric conditions satisfied by these arrays are in accordance with the conditions…
Diversities are a generalization of metric spaces, where instead of the non-negative function being defined on pairs of points, it is defined on arbitrary finite sets of points. Diversities have a well-developed theory. This includes the…
We investigate the typical cycle lengths, the total number of cycles, and the number of finite cycles in random permutations whose probability involves cycle weights. Typical cycle lengths and total number of cycles depend strongly on the…
We study completeness in partial differential varieties. We generalize many results from ordinary differential fields to the partial differential setting. In particular, we establish a valuative criterion for differential completeness and…