S-unit points on analytic hypersurfaces

被引:15
作者
Corvaja, P
Zannier, U
机构
[1] Dipartimento Matemat & Informat, I-33100 Udine, Italy
[2] Scuola Normale Super Pisa, I-56100 Pisa, Italy
来源
ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE | 2005年 / 38卷 / 01期
关键词
D O I
10.1016/j.ansens.2004.09.003
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In analogy with algebraic equations with S-units, we shall deal with S-unit points in an analytic hypersurface, or more generally with values of analytic functions at S-unit points. After proving a general theorem, we shall give diophantine applications to certain problems of integral points on subvarieties of A(1) x G(m)(n). Also, we shall prove an analogue of a theorem of Masser, important in Mahler's method for transcendence. In the course of the proofs we shall also develop a theory for those algebraic subgroups of G(m)(n) whose Zariski closure in A(n) contains the origin. Among others, we shall prove a structure theorem for the family of such subgroups contained in a given analytic hypersurface, obtaining conclusions similar to the case of algebraic varieties. (c) 2005 Elsevier SAS.
引用
收藏
页码:76 / 92
页数:17
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