Conductor-Discriminant Inequality for Hyperelliptic Curves in Odd Residue Characteristic
Conductor-Discriminant Inequality for Hyperelliptic Curves in Odd Residue Characteristic
复制标题
奇剩余特性中超椭圆曲线的导体判别不等式
DOI：
10.1093/imrn/rnad173
复制
发表时间：
2019
影响因子：
1
通讯作者：
P. Srinivasan
中科院分区：
文献类型：
--
作者：
Andrew Obus;P. Srinivasan
本文证明了特征不为2的完备剩余域的离散域K上的超椭圆曲线的导子与判别式之间的一个不等式。具体地说，如果这样的曲线由$y^{2} = f（x）$给出，其中$f（x）\in \mathcal{O}_{K}[x]$，并且如果$\mathcal{X}$是它在$\mathcal{O}_{K}$上的最小正则模型，则$\mathcal{X}$的Artin导体的负值（因此也是$\mathcal{X}$的特殊纤维的不可约分量的数量）由$\operatorname{disc}（f）$的赋值上界。对曲线的亏格或f$的分裂域的分支没有限制。这概括了Ogg，Saito，Liu和第二作者的早期工作。
We prove an inequality between the conductor and the discriminant for all hyperelliptic curves defined over discretely valued fields $K$ with perfect residue field of characteristic not $2$. Specifically, if such a curve is given by $y^{2} = f(x)$ with $f(x) \in \mathcal{O}_{K}[x]$, and if $\mathcal{X}$ is its minimal regular model over $\mathcal{O}_{K}$, then the negative of the Artin conductor of $\mathcal{X}$ (and thus also the number of irreducible components of the special fiber of $\mathcal{X}$) is bounded above by the valuation of $\operatorname{disc}(f)$. There are no restrictions on genus of the curve or on the ramification of the splitting field of $f$. This generalizes earlier work of Ogg, Saito, Liu, and the second author.
局部域上的超椭圆曲线的算术
影响因子：
1.4
作者：
Dokchitser T
通讯作者：
Dokchitser T
投影线模型上除数的显式最小嵌入分辨率
影响因子：
0.8
作者：
Obus, Andrew;Srinivasan, Padmavathi
通讯作者：
Srinivasan, Padmavathi