论文标题
明确的Vologodsky集成曲线
Explicit Vologodsky Integration for Hyperelliptic Curves
论文作者
论文摘要
Vologodsky的$ p $ - adic集成理论在计算几种有趣的算术几何形状中的几个有趣的不变性方面起着核心作用。与科尔曼（Coleman）开发的理论相反，它具有对$ p $的减少类型不敏感的优势。在Besser和Zerbes的最新工作的基础上，我们描述了一种用于计算不良还原性过纤维曲线的Vologodsky积分的算法。这将先前与Katz的联合工作扩展到了所有Meromormormormormorphic差异形式。我们用在Sage中计算的数值示例来说明我们的算法。
Vologodsky's theory of $p$-adic integration plays a central role in computing several interesting invariants in arithmetic geometry. In contrast with the theory developed by Coleman, it has the advantage of being insensitive to the reduction type at $p$. Building on recent work of Besser and Zerbes, we describe an algorithm for computing Vologodsky integrals on bad reduction hyperelliptic curves. This extends previous joint work with Katz to all meromorphic differential forms. We illustrate our algorithm with numerical examples computed in Sage.
