arXiv subjects

Chia-Liang Sun

Publications and source records attributed to Chia-Liang Sun.

6 recordsLinked to original sources

arXiv2023

Vojta's abc Conjecture for algebraic tori and applications over function fields

We prove Vojta's generalized abc conjecture for algebraic tori over function fields with exceptional sets that can be determined effectively. Additionally, we establish a version of the conjecture for toric varieties. As an application, we investigate the Lang-Vojta Conjecture for varieties of log general type that are ramified covers of $\mathbb G_m^n$ over function fields. In particular, we consider the case of $ \mathbb P^n\setminus D$, where $D$ is an algebraic curve over a function field in $\mathbb P^n$ with $n+1$ irreducible components and $°D\ge n+2$. Our methods also apply to the complex situation, enabling us to find explicit exceptional sets for the corresponding case of Vojta's general abc conjecture (complex version) and the Green-Griffith-Lang conjecture.

math.NT↗

arXiv2021

A truncated second main theorem for algebraic tori with moving targets and applications

We establish a second main theorem for algebraic tori with slow growth moving targets with truncation to level 1. As the first application of this result, we prove the Green-Griffith-Lang conjecture for projective spaces with $n+1$ components in the context of moving targets of slow growth. Then we discuss the integrability of the ring of exponential polynomials in the ring of entire functions as another application.

math.CV↗

arXiv2020

On Pisot's $d$-th root conjecture for function fields and related GCD estimates

We propose a function-field analog of Pisot's $d$-th root conjecture on linear recurrences, and prove it under some "non-triviality" assumption. Besides a recent result of Pasten-Wang on B{ü}chi's $d$-th power problem, our main tool, which is also developed in this paper, is a function-field analog of an GCD estimate in a recent work of Levin and Levin-Wang. As an easy corollary of such GCD estimate, we also obtain an asymptotic result.

math.NT↗

arXiv2016

A Local-Global Equality on Every Affine Variety Admitting Points in an Arbitrary Rank-One Subgroup of a Global Function Field

For every affine variety over a global function field, we show that the set of its points with coordinates in an arbitrary rank-one multiplicative subgroup of this function field is topologically dense in the set of its points with coordinates in the topological closure of this subgroup in the product of the multiplicative group of those local completions of this function field over all but finitely many places.

math.NT↗

arXiv2012

Product of local points of subvarieties of almost isotrivial semi-abelian varieties over a global function field

For a semi-abelian variety over a global function field which is isogenous to an isotrivial one, we show that on the product of local points of a subvariety satisfying a minor condition, the topological closure of a finitely generated subgroup of %the group of its global points cuts out exactly the global points of the subvariety lying in this subgroup. As a corollary, on every non-isotrivial super-singular curve of genus two over a global function field, we conclude that the Brauer-Manin condition cuts out exactly the set of its rational points.

math.NT↗

arXiv2012

Solutions of a Linear Equation in a Subgroup of Units in a Function Field

Over a large class of function fields, we show that the solutions of some linear equations in the topological closure of a certain subgroup of the group of units in the function field are exactly the solutions that are already in the subgroup. This result solves some cases of the function field analog of an old conjecture proposed by Skolem.

math.NT↗