论文标题
过椭圆形曲线的模型和整体差异
Models and Integral Differentials of Hyperelliptic Curves
论文作者
论文摘要
令$ c：y^2 = f（x）$是属$ g \ geq 1 $的过eliptic曲线，定义为完全离散值的字段$ k $，带有整数$ o_k $。在$ c $的某些条件下，当残留特性不是$ 2 $时，我们明确地构建了最小的常规型号，并使用普通杂交$ \ MATHCAL {C}/o_k $ $ c $。在相同的环境中，我们确定了$ c $的整体差异的基础，这是相对偶发层的全局部分的$ o_k $ - 基础，$ cheaf $ω_ {\ Mathcal {c}/o_k} $。
Let $C: y^2=f(x)$ be a hyperelliptic curve of genus $g\geq 1$, defined over a complete discretely valued field $K$, with ring of integers $O_K$. Under certain conditions on $C$, mild when residue characteristic is not $2$, we explicitly construct the minimal regular model with normal crossings $\mathcal{C}/O_K$ of $C$. In the same setting we determine a basis of integral differentials of $C$, that is an $O_K$-basis for the global sections of the relative dualising sheaf $ω_{\mathcal{C}/O_K}$.
