國立清華大學 數學系

Abstract: Abelian varieties in positive characteristic are classified by an invariant called Newton polygon. The most "generic" one is called ordinary and the most "special" one is called supersingular. For an abelian variety A over a number field, it is expected that there are lots of primes of K for which A has ordinary reduction. On the other hand, it is also believed that A has infinitely many supersingular primes. Elikes showed that any elliptic curve over K admits infinitely many primes. A general question asked whether every Newton polygon appears in the reduction of A for some prime. In this talk we give a negeative answer to this general question. This is joint work with Jinagwei Xue. Tea Time: 3:30PM, R707