Masser, David and Zannier, Umberto. (2015) Torsion points on families of abelian surfaces and Pell's equation over polynomial rings. Journal of the European Mathematical Society, 17 (9). pp. 23792416.
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Official URL: http://edoc.unibas.ch/41298/
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Abstract
In recent papers we proved a special case of a variant of Pink's Conjecture for a variety inside a semiabelian scheme: namely for any curve inside anything isogenous to a product of two elliptic schemes. Here we go beyond the elliptic situation by settling the crucial case of any simple abelian surface scheme defined over the field of algebraic numbers, thus confirming an earlier conjecture of ShouWu Zhang. This is of particular relevance in the topic, also in view of very recent counterexamples by Bertrand. Furthermore there are applications to the study of Pell equations over polynomial rings; for example we deduce that there are at most finitely many complex t for which there exist A,B≠0 in C[X] with A2–DB2=1 for D=X6+X+t. We also consider equations A2–DB2=c′X+c, where the situation is quite different.
Faculties and Departments:  05 Faculty of Science > Departement Mathematik und Informatik 05 Faculty of Science > Departement Mathematik und Informatik > Ehemalige Einheiten Mathematik & Informatik > Zahlentheorie (Masser) 

UniBasel Contributors:  Masser, David 
Item Type:  Article, refereed 
Article Subtype:  Research Article 
Publisher:  EMS 
ISSN:  14359855 
Note:  Publication type according to Uni Basel Research Database: Journal article 
Identification Number: 

Last Modified:  25 Aug 2016 07:08 
Deposited On:  25 Aug 2016 07:08 
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