Bounds for 2-Selmer ranks in terms of a modified ideal class group2022.02.14
- 2021-10-13 (16:00 ~ 18:00)
October13 (Wednesday) 2021, 16:00 – 18:00,via Zoom
▶Speaker : Myungjun Yu (KIAS, CMC)
▶Title : Bounds for 2-Selmer ranks in terms of a modified ideal class group
Let E be an elliptic curve over the rational number field Q.
Selmer Groups and Ideal Class Groups are important and widely-studied objects in number theory.
Brumer and Kramer studied relations between these two objects in their paper in 1977.
They actually found an upper bound for the 2-Selmer rank of E in terms of the ideal class group of a certain cubic field extension of Q.
As an application, they determined the Mordell-Weil ranks of (most) elliptic curves of prime conductor assuming BSD conjecture.
In this talk, we will talk about a generalization of Brumer-Kramer’s work to the case of elliptic curves over an arbitrary number field.
We will give both upper and lower bounds for the 2-Selmer rank in terms of a (modified) ideal class group,
and the bounds turn out to be sharp in many cases. This is joint work with Hwajong Yoo.
* 주제 : Bounds for 2-Selmer ranks in terms of a modified ideal class group – Myungjun Yu – BRL Seminar
▶회의일시: 2021.10.13. (16:00~)
▶ Zoom링크 : https://unist-kr.zoom.us/j/3877572111?pwd=dDlxWjlNTElxM0NqRVpaMHN2M1JzZz09
▶ 회의 ID : 387 757 2111
▶ 회의 암호 : 456123
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