Mass formula and Oort's conjecture for supersingular abelian threefolds
Mass formula and Oort's conjecture for supersingular abelian threefolds
复制标题
超奇异阿贝尔三重的质量公式和奥尔特猜想
DOI：
10.1016/j.aim.2021.107812
复制
发表时间：
2021
影响因子：
1.7
通讯作者：
Yu Chia-Fu
中科院分区：
文献类型：
--
作者：
Karemaker Valentijn;Yobuko Fuetaro;Yu Chia-Fu
Katsura和Oort得到了3次Siegel模簇的超奇异轨迹S 3，1的类数的显式刻画。在本文中，我们研究了S 3，1的另一种分层，即所谓的群体分层。我们证明了当p-≠2时，有11个层次(a-数字3中的一个，a-数字2中的两个和a-数字1中的8个)。我们给出了每一层的一个显式质量公式，并对a-1的每一层上可能的自同构群进行了分类。在最大开层上，我们证明了每个自同构群是{±1}当且仅当p≠2；即，我们证明了Oort关于一般超奇异交换三重自同构群的猜想在p>；2时精确成立。
Katsura and Oort obtained an explicit description of the supersingular locus S 3, 1 of the Siegel modular variety of degree 3 in terms of class numbers. In this paper we study an alternative stratification of S 3, 1, the so-called mass stratification. We show that when p≠ 2, there are eleven strata (one of a-number 3, two of a-number 2 and eight of a-number 1). We give an explicit mass formula for each stratum and classify possible automorphism groups on each stratum of a-number one. On the largest open stratum we show that every automorphism group is {±1} if and only if p≠ 2; that is, we prove that Oort's conjecture on the automorphism groups of generic supersingular abelian threefolds holds precisely when p> 2.