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Colloquium
Seminar information archive ～04/06｜Next seminar｜Future seminars 04/07～
| Organizer(s) | AIDA Shigeki (chair), IKE Yuichi, IMAI Naoki, HAYASHI Shuhei |
|---|---|
| URL | https://www.ms.u-tokyo.ac.jp/seminar/colloquium_e/index_e.html |
2026/04/24
15:30-16:30 Room #NISSAY Lecture Hall(大講義室) (Graduate School of Math. Sci. Bldg.)
Yukako Kezuka (Graduate School of Mathematical Sciences, The University of Tokyo)
A Birch–Swinnerton-Dyer dichotomy (日本語)
Yukako Kezuka (Graduate School of Mathematical Sciences, The University of Tokyo)
A Birch–Swinnerton-Dyer dichotomy (日本語)
[ Abstract ]
The aim of this talk is to explore a possible weakening of the Birch–Swinnerton-Dyer conjecture, framed as a dichotomy, in which neither the equality of the analytic and Mordell–Weil ranks nor the finiteness of the Tate–Shafarevich group is assumed to hold individually, but rather that if one fails, then so does the other – and in a very specific way. We will explain our motivations coming from (1) the analogy with Iwasawa theory, (2) connections with known results onelliptic curves, and (3) comparison with the function field case.
This talk is based on joint work with Don Zagier (MPIM Bonn).
The aim of this talk is to explore a possible weakening of the Birch–Swinnerton-Dyer conjecture, framed as a dichotomy, in which neither the equality of the analytic and Mordell–Weil ranks nor the finiteness of the Tate–Shafarevich group is assumed to hold individually, but rather that if one fails, then so does the other – and in a very specific way. We will explain our motivations coming from (1) the analogy with Iwasawa theory, (2) connections with known results onelliptic curves, and (3) comparison with the function field case.
This talk is based on joint work with Don Zagier (MPIM Bonn).
