We study the main open parts of the Kawaguchi--Silverman Conjecture, asserting that for a
birational self-map $ f $ of a smooth projective variety $ X $ defined over $\overline {\mathbb …

In this paper, we study arithmetic dynamics in arbitrary characteristic, in particular in positive
characteristic. Applying the arithmetic degree and canonical height in positive characteristic …

arXiv:2311.16369v1 [math.AG] 27 Nov 2023 Page 1 arXiv:2311.16369v1 [math.AG] 27 Nov
2023 ADVANCES IN THE EQUIVARIANT MINIMAL MODEL PROGRAM AND THEIR …

Soit φ: X⤏ X une application rationnelle dominante d'une variété lisse et soit x∈ X, tous
deux définis sur ℚ. Le degré dynamique δ (φ) mesure la complexité géométrique des …

Let $ f $ be a dominant endomorphism of a smooth projective surface $ X $ over an
algebraically closed field $\mathbf {k} $ of characteristic $0 $. We prove that if there is no …

Consider the action of an algebraic group $ G $ on an irreducible algebraic variety $ X $ all
defined over a field $ k $. M. Rosenlicht showed that orbits in general position in $ X $ can …

Motivated by work of Zhang from the early90s, Medvedev and Scanlon formulated the
following conjecture. Let $ K $ be an algebraically closed field of characteristic $0 $ and let …

We prove a conjecture of Medvedev and Scanlon [Ann. of Math.(2), 179 (2014), no. 1, 81–
177] in the case of regular morphisms of semiabelian varieties. That is, if $ G $ is a …

Let $ X $ be a variety defined over an algebraically closed field $ k $ of characteristic $0 $,
let $ N\in\mathbb {N} $, let $ g: X\dashrightarrow X $ be a dominant rational self-map, and let …

Abstract Let f: X→ X be a surjective endomorphism of a normal projective surface. When deg
f≥ 2, applying an (iteration of) f-equivariant minimal model program (EMMP), we determine …