具有极大分歧的 5-adic 亏格二曲线的根数
数论
2021-10-06 v3
摘要
一维阿贝尔簇的局部根数公式是已知的。在本文中，我们通过考虑定义在 -adic 域上且惯性群通过最大可能的有限商（同构于 ）作用于第一 -adic 上同调群的亏格 2 曲线，来处理维度二中最为简单的未知情形。我们给出若干判别此类曲线的准则，并证明了用与 Weierstrass 方程相关的不变量表示的其局部根数公式。
引用
@article{arxiv.2102.07745,
title = {Root numbers of 5-adic curves of genus two having maximal ramification},
author = {Lukas Melninkas},
journal= {arXiv preprint arXiv:2102.07745},
year = {2021}
}
备注
22 pages; major revision: changed the title, deleted the part on elliptic curves (to appear in another submission), changed the formulation of the main result, shortened Section 1, corrected 1.8, merged and shortened Sections 2 and 3, the discussion on discriminants and conductors was rewritten and is now contained in 3.12, the four examples in section 7 were replaced by a new one in 5.9