论文标题
确定第3属CM曲线不良曲线不良的数量
Determining the primes of bad reduction of CM curves of genus 3
论文作者
论文摘要
在本文中，我们引入了一个称为等源性嵌入问题（IEP）的新问题。解决此问题的解决方案的存在与属属$ 3 $的CM曲线不良曲线的数量有关，我们可以在没有解决方案的情况下检测到潜在的良好减少。我们提出了一种用于计算IEP解决方案的算法，并通过不同的曲线系列运行算法。我们能够证明某些特定曲线的降低类型在[LLLR21]中的某些普通曲线上。
In this paper we introduce a new problem called the Isogenous Embedding Problem (IEP). The existence of solutions to this problem is related to the primes of bad reduction of CM curves of genus $3$ and we can detect potentially good reduction in absence of solutions. We propose an algorithm for computing the solutions to the IEP and run the algorithm through different families of curves. We were able to prove the reduction type of some particular curves at certain primes that were open cases in [LLLR21].
