p-twisted Selmer near-companion curves
김도형
27동 325호
0
650
09.04 09:27
| 구분 | 정수론,DASOM |
|---|---|
| 일정 | 2026-09-11(금) 10:30~12:00 |
| 세미나실 | 27동 325호 |
| 강연자 | 김민석 (서울대학교) |
| 담당교수 | 김도형 |
| 기타 |
Title : p-twisted Selmer near-companion curves
Abstract :
Let $E_1$ and $E_2$ be elliptic curves over a number field $K$.
Mazur and Rubin define the concept of $n$-Selmer near-companions and conjecture that
if $E_1$ and $E_2$ are $n$-Selmer near-companions over $K$, then $E_1[n]$ is $G_K$-isomorphic to $E_2[n]$.
Yu proves the conjecture on $n$-Selmer near-companion curves in the case $n=2$.
We introduce the notion of $p$-twisted Selmer near-companions ($p$-TSNC) over $K$ and prove that
if $E_1$ and $E_2$ are $p$-TSNC over $K$, then $K(E_1[p])=K(E_2[p])$ under certain conditions.
