Related papers: Classes logarithmiques et capitulation

We give an introduction to the theory of initial ideals and initial algebras with emphasis on the transfer of structural properties.

Let $G \subset GL(V)$ be a reductive algebraic subgroup acting on the symplectic vector space $W=(V \oplus V^*)^{\oplus m}$, and let $\mu:\ W \rightarrow Lie(G)^*$ be the corresponding moment map. In this article, we use the theory of…

In this article, we focus on orders in arbitrary number fields, consider their Picard groups and finally obtain ring class fields corresponding to them. The Galois group of the ring class field is isomorphic to the Picard group. As an…

Let $p$ be a prime number, $V$ a discrete valuation ring of unequal caracteristics $(0,p)$, $G$ a smooth affine algebraic group over $Spec \,V$. Using partial divided powers techniques of Berthelot, we construct arithmetic distribution…

Let f(t,X) be an irreducible polynomial over the field of rational functions k(t), where k is a number field. Let O be the ring of integers of k. Hilbert's irreducibility theorem gives infinitely many integral specializations of t to values…

We give an alternative proof to the fact that if the square of the infinite radical of the module category of an Artin algebra is equal to zero then the algebra is of finite type by making use of the theory of postprojective and…

In this article, we generalize the arithmetic degree and its related theory to dynamical systems defined over an arbitrary field $\mathbf{k}$ of characteristic $0$. We first consider a dynamical system $(X,f)$ over a finitely generated…

Lie algebras are an important class of algebras which arise throughout mathematics and physics. We report on the formalisation of Lie algebras in Lean's Mathlib library. Although basic knowledge of Lie theory will benefit the reader, none…

We study the l-part of the the wild \'etale kernels WK2i(F) of an arbitary number field F for a given prime l in connection with the logarithmic l-class groups. From the logarithmic arithmetic we deduce rank formulas, periodicity and…

We give a full classification, up to equivalence, of finite-dimensional graded division algebras over the field of real numbers. The grading group is any abelian group.

We study gradings by abelian groups on associative algebras with involution over an arbitrary field. Of particular importance are the fine gradings (that is, those that do not admit a proper refinement), because any grading on a…

We use knowledge of local fields to adapt Jonathan Lubin and Michael Rosen's proof of Mazur's Proposition 4.39. This changes the result about abelian varieties from only working over local fields with a finite residue field to working with…

We describe the mod $p^r$ pro $K$-groups $\{K_n(A/I^s)/p^r\}_s$ of a regular local $\mathbb F_p$-algebra $A$ modulo powers of a suitable ideal $I$, in terms of logarithmic Hodge-Witt groups, by proving pro analogues of the theorems of…

This paper presents a survey of the results and ideas behind the classification of the fine gradings, up to equivalence, on the simple finite dimensional Lie algebras over an algebraically closed field of characteristic zero. It provides an…

We give a survey of recent results related to the problem of characterizing finite-dimensional division algebras by the set of isomorphism classes of their maximal subfields. We also discuss various generalizations of this problem and some…

Given a fine abelian group grading on a finite dimensional simple Lie algebra over an algebraically closed field of characteristic zero, with universal grading group $G$, it is shown that the induced grading by the free group $G/\tor(G)$ is…

In a seminal paper, Stallings introduced folding of morphisms of graphs. One consequence of folding is the representation of finitely-generated subgroups of a finite-rank free group as immersions of finite graphs. Stallings's methods allow…

This work is concerned with regular languages defined over large alphabets, either infinite or just too large to be expressed enumeratively. We define a generic model where transitions are labeled by elements of a finite partition of the…

We establish left and right canonical factorizations of Hilbert-space operator-valued functions G(z) that are analytic on neighborhoods of the complex unit circle and the origin 0, and that have the form G(z)=I+F(z) with F(z) taking…

In this paper, we study the question of classifying self-similar sets under bi-Lipschitz mappings and obtain an important bi-Lipschitz invariant, which is an ideal of a ring related to IFS. Roughly speaking, different Lipschitz equivalence…