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Schmidt's subspace theorem in terms of Seshadri constants for closed subschemes in subgeneral position has been already developed sharply. We derive our theorem for numerically equivalent ample divisors by dint of the above theory step by…

Number Theory · Mathematics 2025-06-16 GuanHeng Zhao

In previous work, the authors established a generalized version of Schmidt's subspace theorem for closed subschemes in general position in terms of Seshadri constants. We extend our theorem to weighted sums involving closed subschemes in…

Number Theory · Mathematics 2023-08-23 Gordon Heier , Aaron Levin

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…

Number Theory · Mathematics 2021-02-08 Emmanuel Breuillard , Nicolas de Saxcé

By analogy with the program of McKinnon-Roth, we define and study approximation constants for points of a projective variety X defined over K the function field of an irreducible and non-singular in codimension 1 projective variety defined…

Algebraic Geometry · Mathematics 2017-02-17 Nathan Grieve

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…

Number Theory · Mathematics 2022-11-15 Si Duc Quang

In this paper, we prove a generalization of the Schmidt's subspace theorem for polynomials of higher degree in subgeneral position with respect to a projective variety over a number field. Our result improves and generalizes the previous…

Number Theory · Mathematics 2022-11-16 Si Duc Quang

We study extensions and generalizations of the Schmidt Subspace Theorem in various settings. In particular, we prove results for algebraic points of bounded degree, giving a sharp version of Schmidt's theorem for quadratic points in the…

Number Theory · Mathematics 2015-11-03 Aaron Levin

The aim of this paper is twofold. The first is to give a quantitative version of Schmidt's subspace theorem for arbitrary families of higher degree polynomials. The second is to give a generalization of the subspace theorem for arbitrary…

Number Theory · Mathematics 2023-08-01 Si Duc Quang

In his 1960 paper, Schmidt studied a quantitative type of Khintchine-Groshev theorem for general (higher) dimensions. Recently, a new proof of the theorem was found, which made it possible to relax the dimensional constraint and more…

Number Theory · Mathematics 2023-03-22 Jiyoung Han

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…

Number Theory · Mathematics 2019-10-18 Yan He , Min Ru

Diophantine approximation explores how well irrational numbers can be approximated by rationals, with foundational results by Dirichlet, Hurwitz, and Liouville culminating in Roth's theorem. Schmidt's subspace theorem extends Roth's results…

Number Theory · Mathematics 2025-02-06 Shivani Goel , Rashi Lunia , Anwesh Ray

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…

Number Theory · Mathematics 2019-12-20 Giang Le

The Subspace Theorem due to Schmidt (1972) is a broad generalisation of Roth's Theorem in Diophantine Approximation (1955) which, in the same way as the latter, suffers a notorious lack of effectivity. This problem is tackled from a…

Number Theory · Mathematics 2024-11-14 Faustin Adiceam , Victor Shirandami

In this paper, we establish a Schmidt's subspace theorem for moving hypersurfaces in weakly subgeneral position. Our result generalizes the previous results on Schmidt's theorem for the case of moving hypersurfaces.

Number Theory · Mathematics 2018-08-30 Si Duc Quang

It was discovered that there is a formal analogy between Nevanlinna theory and Diophantine approximation. Via Vojta's dictionary, the Second Main Theorem in Nevanlinna theory corresponds to Schmidt's Subspace Theorem in Diophantine…

Number Theory · Mathematics 2017-11-28 Nguyen Thanh Son , Tran Van Tan , Nguyen Van Thin

The Schmidt Subspace Theorem affirms that the solutions of some particular system of diophantine approximations in projective spaces accumulates on a finite number of proper linear subspaces. Given a subvariety $X$ of a projective space…

Algebraic Geometry · Mathematics 2007-05-23 Roberto G. Ferretti

We deduce an effective version of Schmidt's subspace theorem on a smooth projective variety X over function fields of characteristic zero for hypersurfaces located in N-subgeneral position with respect to X.

Number Theory · Mathematics 2015-09-25 Giang Le

We prove a generalization of W.M. Schmidt's theorem related to the Diophantine approximations for a linear form of the type $\alpha_1x_1+\alpha_2x_2 +y$ with {\it positive} integers $x_1,x_2$.

Number Theory · Mathematics 2011-12-22 Nikolay G. Moshchevitin

The Schmidt's subspace theory with moving targets, as a significant branch in this field, has been substantially developed in recent years. We continue the approach of the previous work, construct a weighted version of generalized Schmidt…

Number Theory · Mathematics 2026-03-03 GuanHeng Zhao , YuXi Li

It was shown by G. Pisier that any finite-dimensional normed space admits an $\alpha$-regular $M$-position, guaranteeing not only regular entropy estimates but moreover regular estimates on the diameters of minimal sections of its unit-ball…

Functional Analysis · Mathematics 2021-05-28 Emanuel Milman , Yuval Yifrach
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