Ramified primes in the field of definition for the Mordell-Weil group of an elliptic surface

Masato Kuwata
1992 Proceedings of the American Mathematical Society  
Let n : X -> C be an elliptic surface defined over a number field k . We consider the field K in which all the sections are defined. Assuming that thê '-invariant is nonconstant, K is again a number field. We describe the primes of possible ramification of the extension K/k in terms of the configuration of the points of bad fibers in C . Aside from few possible exceptions, K/k is unramified outside of the primes of bad reduction of C and the primes p for which two or more points of bad fibers become identical modulo p .
doi:10.1090/s0002-9939-1992-1116264-0 fatcat:qryvybtz3vaijbk6442ohayzaa