Torsion Points on Curves and -Adic Abelian Integrals

Abstract

THEOREM A. Let f: C --* J be an Albanese morphism defined over a number field K, of a s-mooth curve of genus g into its Jacobian. Suppose J has potential complex multiplication. Let S denote the set of primes p of K satisfying i) p does not divide 2 or 3. ii) K/Q is unramified at P. iii) C has good ordinary reduction over K. Then the set T of torsion points of A defined over an algebraic closure of K which lie on the image of C is defined over an extension of K unramified above S. Moreover #To pg