论文标题
CM Abelian品种的P-Selmer等级
p-Selmer ranks of CM abelian varieties
论文作者
论文摘要
对于在数字字段上具有复杂乘法的椭圆曲线，$ p^{\ infty} $ - Selmer等级甚至适用于所有$ p $。 Česnavičius使用$ e $在复杂的乘法字段中分配并援引已知$ p $ - parity猜想的已知案例时，$ e $在$ p $ spline时就证明了这一点。我们直接证明，并将结果概括为阿贝里亚品种。
For an elliptic curve with complex multiplication over a number field, the $p^{\infty}$--Selmer rank is even for all $p$. Česnavičius proved this using the fact that $E$ admits a $p$-isogeny whenever $p$ splits in the complex multiplication field, and invoking known cases of the $p$-parity conjecture. We give a direct proof, and generalise the result to abelian varieties.
