题目: Growth of Mordeil-Weil ranks in p-adic Lie extensions
时间: 2019年9月27日, 周五 下午16:00-17:30
摘要：A well-known theorem of Mordeil-Weil tells us that the group of F-rational points of an abelian variety is a finitely generated (abelian) group, where F is a number field. One study of the interest lies in the variation of the Mordell-Weil ranks of an abelian variety in a p-adic Lie extension, where here p is a prime. Mazur initiated Iwasawa theory of Selmer groups for abelian varieties with good ordinary reduction at all primes above p, and applied it to obtain an upper bound for the growth of Mordell-Weil ranks in a cyclotomic Zp-extension. In this talk, we will discuss higher analog of such upper bound for the Mordell-Weil rank of an abelian variety with good ordinary reduction at all primes above p in a p-adic Lie extension. Finally, if time permits, we mention the situation of an elliptic curve with supersingular reduction at p. This is joint work with Pin-Chi Hung.