On the supersingular reduction of K3 surfaces with complex multiplication
On the supersingular reduction of K3 surfaces with complex multiplication
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关于复数乘法 K3 曲面的超奇异约简
DOI：
10.1093/imrn/rny210
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发表时间：
2018
影响因子：
1
通讯作者：
Ito Kazuhiro
中科院分区：
文献类型：
--
作者：
Kazuhiro Ito;Tetsushi Ito;Christian Liedtke;Ito Kazuhiro;Ito Kazuhiro
本文研究了具有复数乘法的优良约化模曲面。如果一个复乘曲面具有良好的约化，我们计算了约化的形式Brauer群的Picard数和高度。此外，如果约化是超奇异的，我们在一定的假设下计算了它的Artin不变量。我们的结果推广了Shimada关于Picard数曲面的一些结果.我们的方法依赖于主要定理的复乘法forsurfaces由Rizov，一个明确的描述Breuil-Kisin模块与Lubin-Tate字符由于Andreatta，Goren，霍华德，和Madapusi Pera，和积分比较定理最近成立的Bhatt，莫罗和Scholze。
We study the good reduction moduloofsurfaces with complex multiplication. If asurface with complex multiplication has good reduction, we calculate the Picard number and the height of the formal Brauer group of the reduction. Moreover, if the reduction is supersingular, we calculate its Artin invariant under some assumptions. Our results generalize some results of Shimada forsurfaces with Picard number. Our methods rely on the main theorem of complex multiplication forsurfaces by Rizov, an explicit description of the Breuil–Kisin modules associated with Lubin–Tate characters due to Andreatta, Goren, Howard, and Madapusi Pera, and the integral comparison theorem recently established by Bhatt, Morrow, and Scholze.