Emmanuel Breuillard, Nicolas de Saxcé
We prove a theorem that generalizes Schmidt's Subspace Theorem in the context of metric diophantine approximation. To do so we reformulate the Subspace theorem in the framework of homogeneous dynamics by introducing and studying a slope formalism and the corresponding notion of semistability for diagonal flows.
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The degenerate Schmidt's subspace theorem for moving hypersurface targets
我们的目标是给出运动超曲面目标在射影簇的次一般位置上的Schmidt子空间定理。
A further improvement of the quantitative Subspace Theorem
本文进一步改进了Evertse和Schlickewei关于绝对参数子空间定理的定量版本，结合Schmidt、Faltings和Wuestholz的证明思想，推导出包含丢番图不等式解的子空间数量的更优显式上界。
An effective Schmidt's subspace theorem for hypersurfaces in subgeneral position in projective varieties over function fields
对于位于X的N-次一般位置的超曲面，我们在特征为零的函数域上的光滑射影簇X上推出了Schmidt子空间定理的一个有效形式。
A generalization of the subspace theorem for higher degree polynomials in subgeneral position
本文证明了关于数域上射影簇的次一般位置的高次多项式的Schmidt子空间定理的一个推广。我们的结果改进和推广了Schmidt子空间定理在高次多项式情形下的已有结果。
On the Schmidt Subspace Theorem
我们研究施密特子空间定理在各种设置的扩展和推广。特别是，我们证明结果的代数点的有界程度，给出一个尖锐的版本施密特定理的二次点在射影平面和一个更一般的结果，解决了一个猜想的Schlickewei。
A Schmidt's subspace theorem for moving hyeprplane targets over function fields
本文在函数域上的射影空间中建立了关于移动超平面目标的 Schmidt 子空间定理。
Schmidt's subspace theorem for moving hypersurface in subgeneral position
本文建立了弱次一般位置上活动超曲面的Schmidt子空间定理。我们的结果推广了Schmidt定理在运动超曲面情形下的结果。
We show that affine subspaces of Euclidean space are of Khintchine type for divergence under certain multiplicative Diophantine conditions on the parametrizing matrix. This provides evidence towards the conjecture that all affine subspaces of Euclidean space are of Khintchine type for divergence, or that Khintchine's theorem still holds when restricted to the subspace. This result is proved as a special case of a more general Hausdorff measure result from which the Hausdorff dimension of W(τ) intersected with an appropriate subspace is also obtained.
Recently, Xie-Cao [15] obtained a Second Main Theorem for moving hypersurfaces located in subgeneral position with index which is extended the result of Ru [11]. By using some methods due to Son-Tan-Thin [13], Quang [9] and Xie-Cao [15], we shall give a Schmidt's Subspace Theorem for moving hypersurface targets in subgeneral position with index intersecting algebraic variety. Our result is a extension the Schmidt's Subspace Theorem due to Son-Tan-Thin [13] and Quang [9].
We establish an effective version of Schmidt's subspace theorem on a smooth projective variety $\mathcal{X}$ over function fields of characteristic zero for hypersurfaces located in m-subgeneral position with respect to $\mathcal{X}$. Our result generalizes and improves the results of An-Wang, Ru-Wang and the author.
Schmidt's subspace theorem for moving hypersurface targets
发现Nevanlinna理论与丢番图逼近之间存在形式上的相似性。通过Vojta的字典，Nevanlinna理论中的第二主要定理对应于丢番图逼近中的Schmidt子空间定理。最近，Cherry，Dethloff，and Tan（arXiv：1503.08801v2 [math.CV]）得到了一个关于与射影变量相交的移动超曲面的第二主要定理。本文将给出他们的第二主要定理在丢番图逼近中的对应。
On a theorem of Schmidt's subspace theory with moving targets
本文提出了一种加权的广义施密特子空间理论移动目标版本，作为对相关结果的补充和精确扩展。
Some generalizations of Schmidt's subspace theorem
本文给出了Schmidt子空间定理针对任意高次多项式族的定量版本，并针对射影代数簇中任意闭子概形族提出了该定理的推广。
On the Quantitative Subspace Theorem
本文概述定量子空间定理的最新进展，提出包含“大”解的子空间数量新上界，证明处理“小”解的新间隙原理，并探讨Faltings和Wuestholz的改进及估计剩余解数量的开放难题。
This paper deals with the quantitative Schmidt's subspace theorem and the general from of the second main theorem, which are two correspondence objects in Diophantine approximation theory and Nevanlinna theory. In this paper, we give a new below bound for Chow weight of projective varieties defined over a number field. Then, we apply it to prove a quantitative version of Schmidt's subspace theorem for polynomials of higher degree in subgeneral position with respect to a projective variety. Finally, we apply this new below bound for Chow weight to establish a general form of second main theorem…
Extremal affine subspaces and Khintchine-Jarník type theorems
本文证明Kleinbock猜想，完整分类极值仿射子空间，并给出Khintchine型及Jarník型定理的分类，基于有理点计数新估计，运用多维大筛不等式。
Diophantine approximation and the subspace theorem
本文阐述丢番图逼近中罗斯定理及施密特子空间定理的改进，重点在证明，为有代数数论背景读者提供精简参考，将罗斯定理成果扩展到高维，对丢番图方程和超越理论意义重大。
Probabilistic Effectivity in the Subspace Theorem
针对子空间定理缺乏有效性的问题，本文从概率角度确定有界代数线性形式满足子空间不等式的解的比例，建立相关高度函数估计，并在 Roth 定理情形下细化估计以给出 Waldschmidt 猜想的 Khintchin 型密度版本。
The Many Faces of the Subspace Theorem (after Adamczewski, Bugeaud, Corvaja, Zannier...)
在过去的十年中，子空间定理发现了几个相当意想不到的应用，主要是在丢番图分析和超越理论。在各种各样的壮观的结果，我选择了几个技术上更简单，让人们欣赏如何奇迹般地子空间定理出现在许多情况下，这意味着美丽的解决方案，困难的问题几乎没有人希望解决这么容易。三个主要议题讨论了这篇文章是：工作的Adamczewski和Bugeaud复杂的代数数;工作的Corvaja和Zannier的丢番图方程的权力总和;工作的Corvaja和Zannier积分点的曲线和曲面，以及随后的发展由于莱文和Autissier。特别是，我们给出了一个完整的证明美丽的定理莱文和Autissier：仿射曲面与4个（或更多）适当相交的充分因子在无穷远不能有一个Zebriki密集的整点集。
A generalized Schmidt's subspace theorem for algebraic points of bounded degree
该研究在次一般位置闭子概型的Schmidt子空间定理框架基础上，建立了针对有界次数代数点、关于数值等价丰富除子的Schmidt子空间定理，得到最优因子与广义加权版本，并解决了该领域长期存在的公开猜想。
Combinatorial Applications of the Subspace Theorem
子空间定理是数论中的一个强有力的工具。它以各种形式出现，并随着时间的推移而得到调整和改进。它的应用包括丢番图逼近、代数曲线上整点的结果和超越数的构造。但它的用处超出了数论的范围。子空间定理的其他应用包括线性递归序列和有限自动机。实际上，这些结构彼此之间以及与超越数的构造密切相关。子空间定理也有一些显着的组合应用。本文的目的是给出一个调查的一些这些应用，包括和产品的估计和单位距离的界限。演示文稿将从离散数学家的角度。我们将在下面陈述子空间定理的一些变体，但我们不会证明它们中的任何一个，因为证明超出了这项工作的范围。然而，我们将证明一个简化的特殊情况下的子空间定理，这仍然是非常有用的许多问题，在离散数学。
In this paper, we extend the recent theorem of G. Heier and A. Levin [arXiv:1712.02456] on the generalization of Schmidt's subspace theorem and Cartan's Second Main Theorem in Nevanlinna theory to closed subschemes located in $l$-subgeneral position, using the generic linear combination technique due to Quang.
Rational Points in Hyperbolic Regions and Multiplicative Diophantine Approximation on Manifolds
该研究解决了非退化流形和仿射子空间的乘法丢番图逼近收敛理论问题，改进了相关强极值性结果。
Quantitative Diophantine approximation on affine subspaces
最近，Adiceam，Beresnevich，Levesley，Velani和Zorin证明了非退化流形的Khintchine-Groshev定理收敛情况的定量版本，其动机是应用于干涉对齐。在本文中，我们得到类似的结果仿射子空间。
We prove a generalized version of Schmidt's subspace theorem for closed subschemes in general position in terms of suitably defined Seshadri constants with respect to a fixed ample divisor. Our proof builds on previous work by Evertse and Ferretti, Corvaja and Zannier, and others, and uses standard techniques from algebraic geometry such as notions of positivity, blowing-ups and direct image sheaves. As an application, we recover a higher-dimensional Diophantine approximation theorem of K.F. Roth-type due to D. McKinnon and M. Roth with a significantly shortened proof, while simultaneously ext…
On linear versions of some addition theorems
设K \subset L是域扩张。给定L的K-子空间A，B，研究了由积集AB = {ab| a \in A，b \in B}。我们得到了这个子空间的维数和dim B^n关于dim A，dim B和n的一些下界.这是通过建立线性版本的建设和结果，在加性数论主要是由于肯珀曼和奥尔森。
In this paper we study $p$-adic Diophantine approximation on manifolds, specifically multiplicative Diophantine approximation on affine subspaces and a Diophantine dichotomy for analytic $p$-adic manifolds.
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