论文标题
超ellipriptic曲线的积分差分形式
Integral differential forms for superelliptic curves
论文作者
论文摘要
给定超elipriptic曲线$ y_k：y^n = f（x）$上的本地字段$ k $，我们描述了用于计算$ y_k $ y__k $ in y_k $ on y_k $ in $ y_k $的整体不同形式的新算法的理论背景和实现。我们基于Obus和第二作者的结果，该结果仅使用估值来描述投影线的任意常规模型。我们方法的一种新颖性是，我们构建了一个$ \ Mathcal {o} _k $ - $ y_k $的模型，只有理性的诚意，但可能不是常规的。
Given a superelliptic curve $Y_K : y^n = f(x)$ over a local field $K$, we describe the theoretical background and an implementation of a new algorithm for computing the $\mathcal{O}_K$-lattice of integral differential forms on $Y_K$. We build on the results of Obus and the second author, which describe arbitrary regular models of the projective line using only valuations. One novelty of our approach is that we construct an $\mathcal{O}_K$-model of $Y_K$ with only rational singularities, but which may not be regular.
