Runge's method and modular curves
Language
en
Article de revue
This item was published in
International Mathematics Research Notices. 2011, vol. 9, p. 1997-2027
Oxford University Press (OUP)
English Abstract
We bound the j-invariant of S-integral points on arbitrary modular curves over arbitrary number fields, in terms of the congruence group defining the curve, assuming a certain Runge condition is satisfied by our objects. ...Read more >
We bound the j-invariant of S-integral points on arbitrary modular curves over arbitrary number fields, in terms of the congruence group defining the curve, assuming a certain Runge condition is satisfied by our objects. We then apply our bounds to prove that for sufficiently large prime p, the points of X-0(+) (p(r))(Q) with r > 1 are either cusps or complex multiplication points. This can be interpreted as the non-existence of quadratic elliptic Q-curves with higher prime-power degree.Read less <
Origin
Hal imported