论文标题
非陆上球员和霍奇理论的特殊次要体
Special subvarieties of non-arithmetic ball quotients and Hodge Theory
论文作者
论文摘要
令$γ\ subset \ operatorName {pu}（1，n）$为晶格，$s_γ$是相关的球商。我们证明，如果$s_γ$包含无限的最大绝大部分，那么$γ$是算术的。我们还证明了$S_γ$的斧头猜想，类似于Mok，Pila和Tsimerman最近证明的斧头。证据中的主要成分之一是实现hodge结构两极分化积分变化的时期域内$s_γ$，并将完全的大地次数解释为不太可能的相交。
Let $Γ\subset \operatorname{PU}(1,n)$ be a lattice, and $S_Γ$ the associated ball quotient. We prove that, if $S_Γ$ contains infinitely many maximal totally geodesic subvarieties, then $Γ$ is arithmetic. We also prove an Ax-Schanuel Conjecture for $S_Γ$, similar to the one recently proven by Mok, Pila and Tsimerman. One of the main ingredients in the proofs is to realise $S_Γ$ inside a period domain for polarised integral variations of Hodge structures and interpret totally geodesic subvarieties as unlikely intersections.
