论文标题
SP（2N）中的算术单曲率
Arithmetic Monodromy in Sp(2n)
论文作者
论文摘要
基于Singh-venkataramana的结果，Bajpai--dona-singh-singh给出了一个sp（2n，z）的离散zariski密集亚组的标准。我们适应此标准，以便可以在某些以前被排除的情况下使用。我们将改编的方法应用于SP（6，Z）和SP（4，Z）的亚组，这些方法是作为超几何微分方程的单型组组而产生的。特别是，我们表明，在40个最大一能力的SP（6）中，超过一半是算术的，回答了否定的Katz问题。
Based on a result of Singh--Venkataramana, Bajpai--Dona--Singh--Singh gave a criterion for a discrete Zariski-dense subgroup of Sp(2n,Z) to be a lattice. We adapt this criterion so that it can be used in some situations that were previously excluded. We apply the adapted method to subgroups of Sp(6,Z) and Sp(4,Z) that arise as the monodromy groups of hypergeometric differential equations. In particular, we show that out of the 40 maximally unipotent Sp(6) hypergeometric groups more than half are arithmetic, answering a question of Katz in the negative.
