论文标题
P-ADIC整合不良降低过纤维曲线
p-adic integration on bad reduction hyperelliptic curves
论文作者
论文摘要
在本文中，我们介绍了一种用于计算不良还原性高纤维曲线的P-ADIC积分的算法。对于不良的还原曲线，有两个p-adic整合的概念：伯科维奇 - 科尔曼积分可以在本地执行；和具有理想数字理论特性的Abelian积分。通过通过Annuli和基本的宽开放式覆盖不良的减速曲线，我们将Berkovich-Coleman积分的计算减少到良好还原性高纤维曲线上的已知算法。这些归因于Balakrishnan，Bradshaw和Kedlaya，以及Balakrishnan和Besser分别以良好的还原曲线进行常规和Meromorphic 1形。然后，我们采用了热带几何技术，因为他是拉比诺夫和Zureick-Brown的名字作者，将Berkovich-Coleman积分转换为Abelian积分。我们提供了算法的示例，验证了扭转点之间的某些Abelian积分消失。
In this paper, we introduce an algorithm for computing p-adic integrals on bad reduction hyperelliptic curves. For bad reduction curves, there are two notions of p-adic integration: Berkovich-Coleman integrals which can be performed locally; and abelian integrals with desirable number-theoretic properties. By covering a bad reduction hyperelliptic curve by annuli and basic wide open sets, we reduce the computation of Berkovich-Coleman integrals to the known algorithms on good reduction hyperelliptic curves. These are due to Balakrishnan, Bradshaw, and Kedlaya, and to Balakrishnan and Besser for regular and meromorphic 1-forms on good reduction curves, respectively. We then employ tropical geometric techniques due to the first-named author with Rabinoff and Zureick-Brown to convert the Berkovich-Coleman integrals into abelian integrals. We provide examples of our algorithm, verifying that certain abelian integrals between torsion points vanish.
