Drinfeld modules with no supersingular primes, by Bjorn Poonen

This paper has appeared in Intern. Math. Res. Notices 1998, no. 3, 151-159 and so the dvi version has been removed. We give examples of Drinfeld modules phi of rank 2 and higher over F_q(T) that have no primes of supersingular reduction. The idea is to construct phi so that the associated mod l representations are incompatible with the existence of supersingular primes. We also answer a question of Elkies by proving that such obstructions cannot exist for elliptic curves over number fields.

Bjorn Poonen <poonen@math.princeton.edu>