论文标题
经典的Iwasawa理论和无限下降的阿贝利亚品种
Classical Iwasawa theory and infinite descent on a family of abelian varieties
论文作者
论文摘要
For primes $q \equiv 7 \mod 16$, the present manuscript shows that elementary methods enable one to prove surprisingly strong results about the Iwasawa theory of the Gross family of elliptic curves with complex multiplication by the ring of integers of the field $K = \mathbb{Q}(\sqrt{-q})$, which are in perfect accord with the predictions of the conjecture of Birch和Swinnerton-Dyer。我们还证明了一些与格林伯格经典猜想有关的有趣现象，并给出了旧定理的新证明。
For primes $q \equiv 7 \mod 16$, the present manuscript shows that elementary methods enable one to prove surprisingly strong results about the Iwasawa theory of the Gross family of elliptic curves with complex multiplication by the ring of integers of the field $K = \mathbb{Q}(\sqrt{-q})$, which are in perfect accord with the predictions of the conjecture of Birch and Swinnerton-Dyer. We also prove some interesting phenomena related to a classical conjecture of Greenberg, and give a new proof of an old theorem of Hasse.
