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2017년도 이전 세미나
The local norm map of elliptic curves
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2017-01-13 07:15
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| Category | PMI Number Theory Seminar | ||
|---|---|---|---|
| 날짜 | 2016-06-01 | 시간 | 16:50:00 ~ 18:20:00 |
| 장소 | Math Sci Bldg 404 | Host | YoungJu Choie |
| Speaker | Taekyung Kim | 소속 | Seoul National University |
| TOPIC | The local norm map of elliptic curves | ||
| 소개 및 안내사항 | Suppose that we are given a $p$-adic local number field $K$ and its finite Galois extension $L/K$ with Galois group $G$. For an algebraic group $E$ over $K$, we define its norm map $N: E(L) \to E(K)$ with respect to the extension $L/K$. In particular if $E$ is the multiplicative group, then the cokernel of the norm map $E(K)/NE(L)$ is the abelianized Galois group $G^{ab}$. In the similar fashion, we study the cokernel of the norm map for elliptic curve $E$. We present some techniques to compute the group $E(K)/NE(L)$ according to the ramification conditions of the extension $L/K$ and the reduction types of $E/K$. | ||