论文标题
平面四重奏的局部全球属性
The local-global property for bitangents of plane quartics
论文作者
论文摘要
我们研究了全球田地上平滑四分之一的比利安的算术。借助计算机代数系统并使用Elsenhans - Jahnel在Bitangents的逆Galois问题上的结果，我们表明，在与$ 2 $不同的全球特征领域中，存在在每个本地字段上都有Bitangents，但在全球领域中都没有Bitangents。我们给出了一种算法，以明确查找此类四分之一，并在$ \ mathbb {q} $上举一个示例。我们还讨论了有关对称决定性表示的类似问题。本文是2019年3月的JSiam Jant算法数字理论的第一作者演讲的摘要。细节将出现在其他地方。
We study the arithmetic of bitangents of smooth quartics over global fields. With the aid of computer algebra systems and using Elsenhans--Jahnel's results on the inverse Galois problem for bitangents, we show that, over any global field of characteristic different from $2$, there exist smooth quartics which have bitangents over every local field, but do not have bitangents over the global field. We give an algorithm to find such quartics explicitly, and give an example over $\mathbb{Q}$. We also discuss a similar problem concerning symmetric determinantal representations. This paper is a summary of the first author's talk at the JSIAM JANT workshop on algorithmic number theory in March 2019. Details will appear elsewhere.
