Division-ample sets and the Diophantine problem for rings of integers

关于大域丢番图子集的一个注记

A note on Diophantine subsets of large fields

本文推广了 Fehm 的结果，证明完美大域中无限真子域的仿射平移的有限并集不是丢番图子集，从而回答了 Pop 的问题。

曲面上一个新的丢番图逼近不等式及其应用

A New Diophantine Approximation Inequality on Surfaces and Its Applications

本文证明了曲面上闭子概形的丢番图逼近不等式，推广了Ru-Vojta和Heier-Levin的近期结果，并应用于仿射曲面上的整点退化、最大公因数不等式及S-单位方程，同时在复分析背景下建立了第二主定理型不等式。

Seshadri constants, Diophantine approximation, and Roth's Theorem for arbitrary varieties

In this paper, we associate an invariant $α_{x}(L)$ to an algebraic point $x$ on an algebraic variety $X$ with an ample line bundle $L$. The invariant $α$ measures how well $x$ can be approximated by rational points on $X$, with respect to the height function associated to $L$. We show that this invariant is closely related to the Seshadri constant $ε_{x}(L)$ measuring local positivity of $L$ at $x$, and in particular that Roth's theorem on $\mathbf{P}^1$ generalizes as an inequality between these two invariants valid for arbitrary projective varieties.

某些非交换环上的希尔伯特第十问题

Hilbert's Tenth Problem for some Noncommutative Rings

本文研究两类非交换环上的希尔伯特第十问题，证明扭多项式环及微分多项式环等情形具有否定答案，并建立相关丢番图集与归约关系。