Related papers: Local fields, iterated extensions, and Julia Sets

Let k be an algebraically closed field, let R be an associative k-algebra, and let F = {M_a: a in I} be a family of orthogonal points in R-Mod such that End_R(M_a) = k for all a in I. Then Mod(F), the minimal full sub-category of R-Mod…

Let A be a C*-algebra with real rank zero which has the stable weak cancellation property. Let I be an ideal of A such that I is stable and satisfies the corona factorization property. We prove that 0->I->A->A/I->0 is a full extension if…

Let L/K be a finite Galois extension of complete local fields with finite residue fields and let G=Gal(L/K). Let G_1 and G_2 be the first and second ramification groups. Thus L/K is tamely ramified when G_1 is trivial and we say that L/K is…

Let $K$ be a local field with finite residue field, we define a normal form for Eisenstein polynomials depending on the choice of a uniformizer $\pi_K$ and of residue representatives. The isomorphism classes of extensions generated by the…

We show that an infinite group $G$ definable in a $1$-h-minimal field admits a strictly $K$-differentiable structure with respect to which $G$ is a (weak) Lie group, and show that definable local subgroups sharing the same Lie algebra have…

Let $K$ be a compact set in $\mathbb{C}$, $f$ a function analytic in $\overline{\mathbb{C}}\smallsetminus K$ vanishing at $\infty $. Let $% f\left( z\right) =\sum_{k=0}^{\infty }a_{k}\ z^{-k-1}$ be its Taylor expansion at $\infty $, and…

We generalize Sen theory to extensions $K_\infty/K$ whose Galois group is a $p$-adic Lie group of arbitrary dimension. To do so, we replace Sen's space of $K$-finite vectors by Schneider and Teitelbaum's space of locally analytic vectors.…

This work brings to light some partial \emph{anabelian behaviours} of analytic annuli in the context of Berkovich geometry. More specifically, if $k$ is a valued non-archimedean complete field of mixed characteristic which is algebraically…

Let $k$ be a local field of positive characteristic. Let $L$ be a cocompact discrete subgroup of $k$. Let $U$ be an open compact subgroup of $k$. Let $\ell$, $u$ and $a$ be elements of $k$, with $a$ nonzero. We study the behavior of the…

In [2], an exhaustive construction is achieved for the class of all 4-dimensional unital division algebras over finite fields of odd order, whose left nucleus is not minimal and whose automorphism group contains Klein's four-group. We…

If T is an iteration tree on K and F is a countably certified extender that coheres with the final model of T, then F is on the extender sequence of the final model of T. Several applications of maximality are proved, including: o K…

Let H be the Taft algebra over a finite commutative ring R. When N is a unit in R, we show that all H-cleft extensions over R are determined up to H-comodule algebra isomorphism by their polynomial H-identities.

We present a new method to evaluate the $\alpha'$-expansion of genus-one integrals over open-string punctures and unravel the structure of the elliptic multiple zeta values in its coefficients. This is done by obtaining a simple…

In this paper we develop the theory of the depth of a simple algebraic extension of valued fields $(L/K,v)$. This is defined as the minimal number of augmentations appearing in some Mac Lane-Vaqui\'e chain for the valuation on $K[x]$…

For a given positive integer $n$ and $K/\mathbb{Q}_p$ a finite extension of ramification degree $e$, we determine the number of finite Galois extensions $L/K$ with inertia degree $f$ and a single nonnegative ramification jump at $n$ as long…

Let $K$ be a complete discretely valued field with mixed characteristic $(0, p)$ and imperfect residue field $k_K$. Let $\Delta$ be a finite set. We construct an equivalence of categories between finite dimensional…

The global qualitative behaviour of fields of principal directions for the graph of a real valued polynomial function $f$ on the plane are studied. We provide a Poincar\'e-Hopf type formula where the sum over all indices of the principal…

In recent decades, the defect of finite extensions of valued fields has emerged as the main obstacle in several fundamental problems in algebraic geometry such as the local uniformization problem. Hence, it is important to identify…

When $k$ is a finite field, Becker-Denef-Lipschitz (1979) observed that the total residue map $\text{res}:k(\!(t)\!)\to k$, which picks out the constant term of the Laurent series, is definable in the language of rings with a parameter for…

Let $L/K$ be a finite, totally ramified $p$-extension of complete local fields with residue fields of characteristic $p > 0$, and let $A$ be a $K$-algebra acting on $L$. We define the concept of an $A$-scaffold on $L$, thereby extending and…