4 citations · 21 across the 12 of their papers we have counts for
13 papers
A dynamical Shafarevich theorem for rational maps over number fields and function fields
Lucien Szpiro, Lloyd West
We prove a dynamical Shafarevich theorem on the finiteness of the set of isomorphism classes of rational maps with fixed degeneracies. More precisely, fix an integer d at least 2 a…
Semi-stable Reduction Implies Minimality of the Resultant
Lucien Szpiro, Michael Tepper, Phillip Williams
For a dynamical system on n-dimensional projective space over a number field or a function field, we show that semi-stable reduction implies the minimality of the resultant. We use…
Kunz Regularity Criterion via algebraic entropy
Mahdi Majidi-Zolbanin, Nikita Miasnikov, Lucien Szpiro
In arXiv:1109.6438v1 [math.AG] we introduced and studied a notion of algebraic entropy. In this paper we will give an application of algebraic entropy in proving Kunz Regularity Cr…
Dynamics and entropy in local algebra
Mahdi Majidi-Zolbanin, Nikita Miasnikov, Lucien Szpiro
We introduce and study a notion of algebraic entropy for self-maps of finite length of Noetherian local rings, and develop its properties. We show that it shares the standard prope…
Lifting finite self maps of equicharacteristic complete local rings
Mahdi Majidi-Zolbanin, Nikita Miasnikov, Lucien Szpiro
In the spirit of Fakhruddin (arXiv:math/0212208v1) and Szpiro-Bhatnagar (arXiv:1010.2715v1), we show that for an equicharacteristic complete local ring A, with a given embedding of…
Almost Newton, sometimes Lattès
Benjamin Hutz, Lucien Szpiro
Self-maps everywhere defined on the projective space over a number field or a function field are the basic objects of study in the arithmetic of dynamical systems. One reason…