Topic
Subspace theorem
About: Subspace theorem is a research topic. Over the lifetime, 179 publications have been published within this topic receiving 4391 citations.
Papers published on a yearly basis
Papers
Book•
1 Jan 2006TL;DR: In this paper, the authors present a glossary of notation for algebraic geometry, including the Vojta conjecture, the ABC conjecture, and the subspace theorem of the Weil heights.
Abstract: I. Heights II. Weil heights III. Linear tori IV. Small points V. The unit equation VI. Roth's theorem VII. The subspace theorem VIII. Abelian varieties IX. Neron-Tate heights X. The Mordell-Weil theorem XI. Faltings theorem XII. The ABC-conjecture XIII. Nevanlinna theory XIV. The Vojta conjectures Appendix A. Algebraic geometry Appendix B. Ramification Appendix C. Geometry of numbers Bibliography Glossary of notation Index.
872 citations
Book•
1 Aug 1991
TL;DR: Siegel's lemma and heights, Diophantine approximation, The thue equation, S-unit equations and hyperelliptic equations as discussed by the authors, S-Unit equations in more than two variables
Abstract: Siegel's lemma and heights- Diophantine approximation- The thue equation- S-unit equations and hyperelliptic equations- Diophantine equations in more than two variables
352 citations
TL;DR: In this article, the authors derived an explicit upper bound for A(a 1,.., a n, r) which depends only on the dimension n and on the rank r.
Abstract: Let K be a field of characteristic 0 and let n be a natural number. Let r be a subgroup of the multiplicative group (K*) n of finite rank r. Given a 1 ,...,a n E K* write A(a 1 ,...,a n , Γ) for the number of solutions x = (x 1 ,..., x n ) ∈ Γ of the equation a 1 x 1 +... + a n x n = 1, such that no proper subsum of a 1 x 1 + ...+ a n x n vanishes. We derive an explicit upper bound for A(a 1 ,.., a n , r) which depends only on the dimension n and on the rank r.
256 citations
Journal Article•
TL;DR: In this article, the conditions générales d'utilisation (http://www.compositio.nl/) implique l'accord avec les conditions generales de utilisation, i.e., usage commerciale ou impression systématique, constitutive of an infraction pénale.
Abstract: © Foundation Compositio Mathematica, 1996, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
86 citations
Posted Content•
TL;DR: In this article, it was shown that the integral points on affine surfaces are contained in a curve, and that there are only finitely many quadratic integral points in an affine curve with five points at infinity.
Abstract: We study integral points on affine surfaces by means of a new method, relying on the Subspace Theorem. Under suitable assumptions on the divisor at infinity, we prove that the integral points are contained in a curve. As a corollary, we prove that there are only finitely many quadratic integral points on an affine curve with five points at infinity.
75 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 16 |
| 2020 | 10 |
| 2019 | 17 |
| 2018 | 10 |
| 2017 | 13 |
| 2016 | 5 |