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Finite descent obstruction on curves and modularity
Author(s) -
Helm David,
Voloch José Felipe
Publication year - 2011
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdr015
Subject(s) - mathematics , descent (aeronautics) , pure mathematics , elliptic curve , set (abstract data type) , computer science , engineering , programming language , aerospace engineering
We prove that a form of finite Galois descent obstruction is the only obstruction to the existence of S integral points on integral models of twists of modular curves over Q , for any finite set of primes S . We deduce this from an existence theorem for elliptic curves over Q satisfying certain local conditions.