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- FIELD
- Mathematics
- DATE
-
May 30 (Thu), 2024
- TIME
- 16:00 ~ 17:00
- PLACE
- 1424
- SPEAKER
- Kim, Hansol
- HOST
- Lee, Youngmin
- INSTITUTE
- KAIST
- TITLE
- [GS_M_NT] Growth of torsion groups of elliptic curves over number fields, rational isogenies, and number fields without rationally defined CM
- ABSTRACT
- We find an equivalent condition that a number field $K$ has the following property: There is a prime $p_{K}$ depending only on $K$ such that if $d$ is a positive integer whose minimal prime divisor is greater than $p_{K}$, then for any extension $L/K$ of degree $d$ and any elliptic curve $E/K$, we have $E\left(L\right)_{\operatorname{tors}} = E\left(K\right)_{\operatorname{tors}}$. For the purpose, we study the relations among torsion groups of elliptic curves over number fields, rational isogenies, and number fields without rationally defined CM. As a collorary of our result, we prove that any quadratic number field which is not an imaginary number field whose class number is not $1$ has the above property. This is a joint work with Bo-Hae Im.
- FILE
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