Automorphisms of Supersingular K3 Surfaces and Salem Polynomials
Automorphisms of Supersingular K3 Surfaces and Salem Polynomials
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DOI：
10.1080/10586458.2015.1073641
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发表时间：
2015-03
影响因子：
0.5
通讯作者：
I. Shimada
中科院分区：
文献类型：
--
作者：
I. Shimada
摘要给出了一种生成具有奇特征的超奇异K3曲面的多个自同构的方法。作为应用，我们证明了：如果p是小于或等于7919的奇素数，则特征p中的每个超奇异K3曲面都有一个自同构，其在Néron-Severi格上的特征多项式是22次Salem多项式。对于Artin不变量为10的超奇异K3曲面，对于小于或等于17,389的奇素数也是如此。
Abstract We present a method to generate many automorphisms of a supersingular K3 surface in odd characteristic. As an application, we show that if p is an odd prime less than or equal to 7919, then every supersingular K3 surface in characteristic p has an automorphism whose characteristic polynomial on the Néron–Severi lattice is a Salem polynomial of degree 22. For a supersingular K3 surface with Artin invariant 10, the same holds for odd primes less than or equal to 17, 389.