Related papers: Kawaguchi-Silverman conjecture for int-amplified e…

The purpose of the present paper is to discuss the following conjecture of Fel'shtyn and Hill, which is a generalization of the classical Burnside theorem: Let G be a countable discrete group, f its automorphism, R(f) the number of…

We give a counterexample to the following conjecture: the set of isolated periodic points of an automorphism of degree at least two on an affine space is a set of bounded height. As a positive result, we prove that any cohomologically…

We study the metric compactification of a Kobayashi hyperbolic complex manifold \(\mathcal{X} \) equipped with the Kobayashi distance \( \mathsf{k}_{\mathcal{X}} \). We show that this compactification is genuine -- i.e., \( \mathcal{X} \)…

In this paper, we study the relation between two dynamical systems (V,f) and (V,g) with f. g = g . f. As an application, we show that an endomorphism (respectively a polynomial map with Zariski dense, of bounded Pre(f) has only finitely…

In this paper, we will give suitable conditions on differential polynomials $Q(f)$ such that they take every finite non-zero value infinitely often, where $f$ is a meromorphic function in complex plane. These results are related to Problem…

The aim of the article is an extension of the Monodromy Conjecture of Denef and Loeser in dimension two, incorporating zeta functions with differential forms and targeting all monodromy eigenvalues, and also considering singular ambient…

We prove that the specialization to q=1 of a Kirillov-Reshetikhin module for an untwisted quantum affine algebra of classical type is projective in a suitable category. This yields a uniform character formula for the Kirillov-Reshetikhin…

Let $F$ be a CM number field. We prove modularity lifting theorems for regular $n$-dimensional Galois representations over $F$ without any self-duality condition. We deduce that all elliptic curves $E$ over $F$ are potentially modular, and…

A basic problem in the study of algebraic morphisms is to determine which sets can be realised as the image of an endomorphism of affine space. This paper extends the results previously obtained by the first author on the question of…

Let $X$ be an abelian variety over an algebraically closed field $\mathbf{k}$ and $f$ a quasi-unipotent automorphism of $X$. When $\mathbf{k}$ is the field of complex numbers, Lin, Oguiso, and D.-Q. Zhang provide an explicit formula for the…

Let $E/F$ be an elliptic curve defined over a number field $F$ with complex multiplication by the ring of integers of an imaginary quadratic field $K$ such that the torsion points of $E$ generate over $F$ an abelian extension of $K$. In…

Let $X$ be a Fano type variety and $(X,\Delta)$ be a log Calabi-Yau pair with $\Delta$ a Weil divisor. If $(X,\Delta)$ admits a polarized endomorphism, then we show that $(X,\Delta)$ is a finite quotient of a toric pair. Along the way, we…

The purpose of the present paper is to prove for finitely generated groups of type I the following conjecture of A.Fel'shtyn and R.Hill, which is a generalization of the classical Burnside theorem. Let G be a countable discrete group, f one…

Let $K$ be a field of positive characteristic and $K<x, y>$ be the free algebra of rank two over $K$. Based on the degree estimate done by Y.-C. Li and J.-T. Yu, we extend the results of S.J. Gong and J.T. Yu's results: (1) An element…

Our main result in this article is a proof (under mild technical assumptions) of an analogue for $p$-adic Galois representations attached to a newform $f$ of even weight $k\geq4$ of Kolyvagin's conjecture on the $p$-indivisibility of…

It is shown that for the restricted Zassenhaus algebra $\mathfrak{W}=\mathfrak{W}(1,n)$, $n>1$, defined over an algebraically closed field $\mathbb{F}$ of characteristic 2 any projective indecomposable restricted $\mathfrak{W}$-module has…

Let $f\colon X \dashrightarrow X$ be a birational transformation of a projective manifold $X$ whose Kodaira dimension $\kappa(X)$ is non-negative. We show that, if there exist a meromorphic fibration $\pi \colon X\dashrightarrow B$ and a…

Inspired by Fujita's algebro-geometric result that complex projective space has maximal degree among all K-semistable complex Fano varieties, we conjecture that the height of a K-semistable metrized arithmetic Fano variety X of relative…

Jake Goodman and Ulrich Kr\"ahmer have recently shown that a twisted Calabi-Yau algebra $A$ with modular automorphism $\sigma$ and dimension $d$ can be "untwisted," in the sense that the Ore extensions $A[X;\sigma]$ and $A[X^{\pm1};\sigma]$…

We give a sharp divisibility bound, in terms of g, for the degree of the field extension required to realize the endomorphisms of an abelian variety of dimension g over an arbitrary number field; this refines a result of Silverberg. This…