Towards Lang-Trotter for Elliptic Curves over Function Fields

@inproceedings{Hall2006TowardsLF,
  title={Towards Lang-Trotter for Elliptic Curves over Function Fields},
  author={Chris Hall and Jos{\'e} Felipe Voloch},
  year={2006}
}
Let K be a global field of char p and let Fq ⊂ K denote the algebraic closure of Fp in K. We fix an elliptic curve E/K with non-constant j-invariant and a torsion-free subgroup Σ ⊆ E(K) of rank r > 0. We write V for the open set of places v of K such that the special fiber Ev is an elliptic curve and, for v in V , we let Σv ⊂ Ev(kv) be the image of Σ under reduction modulo v, where kv is the residue field of K at v. We fix a finite set of (rational) prime numbers S which is large enough to… CONTINUE READING