Hecke orbits on Shimura varieties of Hodge type

Autor:	D'Addezio, Marco, van Hoften, Pol
Rok vydání:	2022
Předmět:	Mathematics - Algebraic Geometry Mathematics - Number Theory 11G18 (Primary) 14G35 (Secondary)
Druh dokumentu:	Working Paper
Popis:	We prove the Hecke orbit conjecture of Chai--Oort for Shimura varieties of Hodge type at primes of good reduction, under a mild assumption on the size of the prime. Our proof uses a new generalisation of Serre--Tate coordinates for deformation spaces of central leaves in such Shimura varieties, constructed using work of Caraiani--Scholze and Kim. We use these coordinates to give a new interpretation of Chai--Oort's notion of strongly Tate-linear subspaces of these deformation spaces. This lets us prove upper bounds on the local monodromy of these subspaces using the Cartier--Witt stacks of Bhatt--Lurie. We also prove a rigidity result in the style of Chai--Oort for strongly Tate-linear subspaces. Another main ingredient of our proof is a new result on the local monodromy groups of $F$-isocrystals "coming from geometry", which should be of independent interest. Comment: 61 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2205.10344 Zobrazit plný text záznamu View this record from Arxiv