Xuan Kien Phung

activity

20172026

most citedOn the Garden of Eden theorem for endomorphisms of symbolic algebraic varieties

14 citations · 77 across the 28 of their papers we have counts for

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8 papers · 1 filter

math.AG2021

Weakly surjunctive groups and symbolic group varieties

Xuan Kien Phung

In this paper, we introduce the classes of weakly surjunctive and linearly surjunctive groups which include all sofic groups and more generally all surjunctive groups. We investiga…

math.AG2021★ 2 cited

LEF-groups and endomorphisms of symbolic varieties

Xuan Kien Phung

Let $G$ be a group and let $X$ be an algebraic variety over an algebraically closed field $k$ of characteristic zero. Denote $A = X (k)$ the set of rational points of $X$ . We investig…

math.AG2021

A geometric generalization of Kaplansky's direct finiteness conjecture

Xuan Kien Phung

Let $G$ be a group and let $k$ be a field. Kaplansky's direct finiteness conjecture states that every one-sided unit of the group ring $k [G]$ must be a two-sided unit. In this pape…

math.AG2019★ 3 cited

Large unions of generalized integral sections on elliptic surfaces

Xuan Kien Phung

Let $f : X \to B$ be a nonisotrivial complex elliptic surface and let $D \subset X$ be an integral divisor dominating $B$ . We study finiteness related properties of…

math.AG2019

Finiteness criteria and uniformity of integral sections in some families of abelian varieties

Xuan Kien Phung

Let $A$ be abelian variety over the function field $K$ of a compact Riemann surface $B$ . Fix a model $f : A \to B$ of $A / K$ and a certain effective horizontal diviso…

math.AG2019★ 1 cited

On Parshin-Arakelov theorem and uniformity of $S$ -integral sections on elliptic surfaces

Xuan Kien Phung

Let $f : X \to B$ be a complex elliptic surface and let $\DD \subset X$ be an integral divisor dominating $B$ . It is well-known that the Parshin-Arakelov theorem implies the M…

math.AG2019★ 1 cited

Generalized integral points on abelian varieties and the Geometric Lang-Vojta conjecture

Xuan Kien Phung

Let $A$ be an abelian variety over the function field $K$ of a compact Riemann surface $B$ . Fix a model $f : A \to B$ of $A / K$ and an effective horizontal divisor $\…

math.AG2017

On injective endomorphisms of symbolic schemes

Tullio Ceccherini-Silberstein, Michel Coornaert, Xuan Kien Phung

Building on the seminal work of Gromov on endomorphisms of symbolic algebraic varieties [10], we introduce a notion of cellular automata over schemes which generalize affine algebr…

Weakly surjunctive groups and symbolic group varieties

LEF-groups and endomorphisms of symbolic varieties

A geometric generalization of Kaplansky's direct finiteness conjecture

Large unions of generalized integral sections on elliptic surfaces

Finiteness criteria and uniformity of integral sections in some families of abelian varieties

On Parshin-Arakelov theorem and uniformity of S-integral sections on elliptic surfaces

Generalized integral points on abelian varieties and the Geometric Lang-Vojta conjecture

On injective endomorphisms of symbolic schemes

On Parshin-Arakelov theorem and uniformity of $S$ -integral sections on elliptic surfaces