论文标题
Selmer组的多重性和Artin Twist的根号
Multiplicities in Selmer groups and root numbers for Artin twists
论文作者
论文摘要
令$ k/f $为数字字段的有限galois扩展名，$σ$是$ \ mathrm {gal}（k/f）$的绝对不可约，自动划分表示。让$ p $是一个奇怪的素数，考虑两条椭圆曲线$ e_1，e_2 $，良好，普通降低，以高于$ p $和同等的mod- $ p $ galois表示形式。在本文中，我们研究了与$ p^\ infty $ -selmer组相关的表示空间中$σ$ $σ$ $σ$的均等差异。我们还将$ e_i/f $ $σ$的扭曲的根号（$ p $ - parity的猜想都具有$ e_1/f $ by $σ$时的扭曲时，并且仅在$ e_2/f $ $σ$时。我们还用某些当地的伊瓦沙瓦（Iwasawa）不变式来表达Mazur-Rubin-Neková列的算术本地常数。
Let $K/F$ be a finite Galois extension of number fields and $σ$ be an absolutely irreducible, self-dual representation of $\mathrm{Gal}(K/F)$. Let $p$ be an odd prime and consider two elliptic curves $E_1, E_2$ with good, ordinary reduction at primes above $p$ and equivalent mod-$p$ Galois representations. In this article, we study the variation of the parity of the multiplicities of $σ$ in the representation space associated to the $p^\infty$-Selmer group of $E_i$ over $K$. We also compare the root numbers for the twist of $E_i/F$ by $σ$ and show that the $p$-parity conjecture holds for the twist of $E_1/F$ by $σ$ if and only if it holds for the twist of $E_2/F$ by $σ$. We also express Mazur-Rubin-Nekovář's arithmetic local constants in terms of certain local Iwasawa invariants.
