超星阿贝尔变体的 Theta 空值

IF 0.6 4区数学 Q4 COMPUTER SCIENCE, THEORY & METHODS

Journal of Symbolic Computation Pub Date : 2023-12-29 DOI:10.1016/j.jsc.2023.102296

Andreas Pieper

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引用次数: 0

摘要

我们给出了一个充分标准，它允许有效地计算 ker(η)的最大各向同性子群方案对 Eg 的任何商的 theta 空值。我们用我们的方法实现了一种计算 3 属超星曲线的算法。

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Theta nullvalues of supersingular Abelian varieties

Let η be a polarization with connected kernel on a superspecial abelian variety $E^{g}$ . We give a sufficient criterion which allows the computation of the theta nullvalues of any quotient of $E^{g}$ by a maximal isotropic subgroup scheme of $\ker (η)$ effectively.

This criterion is satisfied in many situations studied by Li and Oort (1998). We used our method to implement an algorithm that computes supersingular curves of genus 3.

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来源期刊

Journal of Symbolic Computation 工程技术-计算机：理论方法

CiteScore

2.10

自引率

14.30%

发文量

审稿时长

142 days

期刊介绍： An international journal, the Journal of Symbolic Computation, founded by Bruno Buchberger in 1985, is directed to mathematicians and computer scientists who have a particular interest in symbolic computation. The journal provides a forum for research in the algorithmic treatment of all types of symbolic objects: objects in formal languages (terms, formulas, programs); algebraic objects (elements in basic number domains, polynomials, residue classes, etc.); and geometrical objects. It is the explicit goal of the journal to promote the integration of symbolic computation by establishing one common avenue of communication for researchers working in the different subareas. It is also important that the algorithmic achievements of these areas should be made available to the human problem-solver in integrated software systems for symbolic computation. To help this integration, the journal publishes invited tutorial surveys as well as Applications Letters and System Descriptions.