CM liftings of surfaces over finite fields and their applications to the Tate conjecture
CM liftings of surfaces over finite fields and their applications to the Tate conjecture
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有限域上曲面的 CM 提升及其在泰特猜想中的应用
DOI：
10.1017/fms.2021.24
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Koshikawa Teruhisa
中科院分区：
文献类型：
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作者：
Ito Kazuhiro;Ito Tetsushi;Koshikawa Teruhisa
给出了正交Shimura簇的积分正则模型和Kuga-Satake态射在有限域上曲面算术中的应用。我们证明了有限域上的每一个有限高的曲面都有一个特征提升，其一般纤维是一个具有复数乘法的曲面。结合Mukai和Buskin的结果，证明了有限域上曲面平方的Tate猜想。为了获得这些结果，我们构造一个类似的Kisin的代数群的表面的有限高度和构造特征提升的表面保持行动的环面的代数群。我们得到这些结果的曲面在有限域上的任何特征，包括那些特征或。
We give applications of integral canonical models of orthogonal Shimura varieties and the Kuga-Satake morphism to the arithmetic of surfaces over finite fields. We prove that every surface of finite height over a finite field admits a characteristic lifting whose generic fibre is a surface with complex multiplication. Combined with the results of Mukai and Buskin, we prove the Tate conjecture for the square of a surface over a finite field. To obtain these results, we construct an analogue of Kisin’s algebraic group for a surface of finite height and construct characteristic liftings of the surface preserving the action of tori in the algebraic group. We obtain these results for surfaces over finite fields of any characteristics, including those of characteristic or .