论文标题
不太可能与Bruhat地层的交集
Unlikely Intersections with Bruhat Strata
论文作者
论文摘要
令$ \ Mathcal {a} _ {g} $为$ g $的模块空间，主要是极化的Abelian品种，而不是$ \ Mathbb {Z} $，然后让$ \ \ \ Mathcal {t} \ subset {t} \ subset \ mathcal \ natercal {a} _} _ {g} $ n over n over n over n ovel $ n over $ n over $ c;在不太可能的交点猜想的动机中，我们研究了$ \ Mathcal {t} _ {\ Mathbb {f} _ {p}} $与$ \ Mathcal {a} _} _ {a} _ {g，\ mathbb {f} f} $ {这些层的特征是纤维的$ p $ torsion中存在某些亚组方案。我们发现，从$ \ Mathcal {t} _ {\ Mathbb {f} _ {p}} $的$ \ Mathcal {t} _ {\ Mathbb {p}} $与此类分层的相交的相交的相互作用的相互作用的相互作用的相互作用均由$ \ Mathcal Inters的$ \ Mathcal { $ \ MATHCAL {A} _ {G} $。该结果概括为所有Abelian型Shimura品种以及配备某些动机数据的Hodge结构的变化。此外，它提供了另一个例子，说明了特征零的功能超越原理如何用于研究积极特征中不太可能的交集，这是在作者最近的作品基础上基于作者的最新作品。
Let $\mathcal{A}_{g}$ be the moduli space of $g$-dimensional principally polarized abelian varieties over $\mathbb{Z}$, and let $\mathcal{T} \subset \mathcal{A}_{g}$ be a closed locus, also defined over $\mathbb{Z}$. Motivated by unlikely intersection conjectures, we study the intersection of $\mathcal{T}_{\mathbb{F}_{p}}$ with the Bruhat strata in $\mathcal{A}_{g,\mathbb{F}_{p}}$ as $p$-varies; these are strata characterized by the existence of certain subgroup schemes inside the $p$-torsion of the fibres. We find that, away from a finite set of primes, positive-dimensional ``unlikely'' intersections of $\mathcal{T}_{\mathbb{F}_{p}}$ with such strata are all accounted for by intersections of $\mathcal{T}$ with special loci inside $\mathcal{A}_{g}$. This result generalizes to all abelian-type Shimura varieties, and variations of Hodge structures equipped with certain motivic data. It moreover gives another example of how functional transcendence principles in characteristic zero can be used to study unlikely intersections in positive characteristic, building on recent work by the author.
