Logo der Universität Basel

Research Database / FORSCHUNGSDATENBANK 
PRINTDOC
 
Publication 162112 | Verified
 

Data Entry: Please note that the research database will be replaced by UNIverse by the end of October 2023. Please enter your data into the system https://universe-intern.unibas.ch. Thanks

Login for users with Unibas email account...

Login for registered users without Unibas email account...

 
Problème de Mordell-Lang modulo certaines sous-variétés abéliennes
JournalArticle (Originalarbeit in einer wissenschaftlichen Zeitschrift)
 
ID 162112
Author(s) Rémond, Gaël; Viada, Evelina
Author(s) at UniBasel Viada, Evelina
Year 2003
Title Problème de Mordell-Lang modulo certaines sous-variétés abéliennes
Journal International Mathematics Research Notices
Volume 2003
Number 35
Pages / Article-Number 1915-1931
Abstract Following a result of Bombieri, Masser and Zannier on tori, the second author proved that the intersection of a transversal curve C in a power A of a C. M. elliptic curve with the union of all algebraic subgroups of Eg of codimension 2 is finite. Here transversal means that C is not contained in any translate of an algebraic subgroup of codimension 1. We merge this result with Faltings’ theorem that C ∩ Γ is finite when Γ is a finite rank subgroup of A. We obtain the finiteness of the intersection of C with the union of all Γ + B for B an abelian subvariety of codimension 2. As a corollary, we generalize the previous result to a curve C not contained in any proper algebraic subgroup, but possibly contained in a translate. We also have weaker analog results in the non C. M. case.
Publisher Oxford University Press
ISSN/ISBN 1073-7928 ; 1687-0247
edoc-URL http://edoc.unibas.ch/dok/A5260091
Full Text on edoc Available
Digital Object Identifier DOI 10.1155/S1073792803130164
ISI-Number WOS:000184411700002
Document type (ISI) Article
 
   

MCSS v5.8 PRO. 0.362 sec, queries - 0.000 sec ©Universität Basel  |  Impressum   |    
02/05/2024