论文标题
Hecke Orbits on Hodge类型的Shimura品种
Hecke orbits on Shimura varieties of Hodge type
论文作者
论文摘要
我们证明了Hecke的chai的Hecke Orbit猜想 - 奇数质量良好的杂种类型的Shimura品种。我们为$ f $ - 异晶体“来自几何形状”的本地单片组使用了新的结果，该小组优化了机组人员的抛物线猜想。在证据的过程中，我们还引入了对中央叶子正式社区的串行坐标的非共同概括，这是基于先前的Caraiani-Scholze和Kim的作品。使用这些坐标，我们重新诠释了柴 - OORT强烈的泰特线性子空间的概念，并为它们的单型组建立了上限。在此步骤中，我们采用了卡地亚（Cartier）的概念 - 韦特（Witt）堆栈，如德林菲尔德（Drinfeld）和巴特（Bhatt）所述。证据中的另一种关键成分是柴伊奥尔特证明的刚度结果，这表明相关子空间是强烈的泰特线性。在途中，我们将de de jong的全部忠诚定理概括为$ f $ isocrystals。
We prove the Hecke orbit conjecture of Chai--Oort for Shimura varieties of Hodge type at odd primes of good reduction. We use a novel result for the local monodromy groups of $F$-isocrystals "coming from geometry", which refines Crew's parabolicity conjecture. In the course of the proof, we also introduce a noncommutative generalisation of Serre--Tate coordinates for formal neighbourhoods of central leaves, built upon the previous work of Caraiani--Scholze and Kim. Using these coordinates, we reinterpret Chai--Oort's notion of strongly Tate-linear subspaces and we establish upper bounds for their monodromy groups. For this step, we employ the notion of Cartier--Witt stacks, as introduced by Drinfeld and Bhatt--Lurie. Another crucial ingredient in the proof is a rigidity result proved by Chai--Oort, which shows that the relevant subspaces are strongly Tate-linear. On the way, we generalise de Jong's full faithfulness theorem for $F$-isocrystals.
