Geodesic
Torsion points on families of simple abelian surfaces and Pell's equation over polynomial rings (with an appendix by E. V. Flynn)
Journal of the European Mathematical Society, Tome 17 (2015) no. 9, pp. 2379-2416 Cet article a éte moissonné depuis la source EMS Press

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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 Shou-Wu 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.
DOI : 10.4171/jems/560
Classification : 11-XX, 14-XX
Keywords: Torsion point, abelian surface scheme, Pell equation, Jacobian variety, Chabauty’s theorem 
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     author = {David Masser and Umberto Zannier},
     title = {Torsion points on families of simple abelian surfaces and {Pell's} equation over polynomial rings (with an appendix by {E.} {V.} {Flynn)}},
     journal = {Journal of the European Mathematical Society},
     pages = {2379--2416},
     year = {2015},
     volume = {17},
     number = {9},
     doi = {10.4171/jems/560},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/560/}
}
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David Masser; Umberto Zannier. Torsion points on families of simple abelian surfaces and Pell's equation over polynomial rings (with an appendix by E. V. Flynn). Journal of the European Mathematical Society, Tome 17 (2015) no. 9, pp. 2379-2416. doi: 10.4171/jems/560

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