2-Selmer parity for hyperelliptic curves in quadratic extensions
2-Selmer parity for hyperelliptic curves in quadratic extensions
复制标题
二次扩张中超椭圆曲线的 2-Selmer 宇称
DOI：
10.1112/plms.12565
复制
发表时间：
2023
影响因子：
1.8
通讯作者：
Morgan A
中科院分区：
文献类型：
--
作者：
Morgan A
研究了数域上超椭圆曲线Jacobian的2-奇偶猜想。在对它们的约化作一些适当的假设下，我们证明了关于基域的二次扩张的猜想。证明是通过推广与曲线局部不变量相关的克雷默和通内尔公式进行的，这可能是独立感兴趣的。一个新的特点，这一概括是外观的条款，管理是否卡塞尔-泰特配对的雅可比矩阵是交替的，这首先出现在工作的Poonen斯托尔。我们在许多情况下建立的本地公式，并表明，在其余的情况下，它遵循标准的全球astronautures。
We study the 2‐parity conjecture for Jacobians of hyperelliptic curves over number fields. Under some mild assumptions on their reduction, we prove the conjecture over quadratic extensions of the base field. The proof proceeds via a generalisation of a formula of Kramer and Tunnell relating local invariants of the curve, which may be of independent interest. A new feature of this generalisation is the appearance of terms which govern whether or not the Cassels–Tate pairing on the Jacobian is alternating, which first appeared in work of Poonen–Stoll. We establish the local formula in many instances and show that in remaining cases, it follows from standard global conjectures.