Towards a p-adic nowhere density conjecture of Hecke Orbits

2025/06/07 by Yu Fu, Fu, Yu
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Advanced Mathematical Identities

paper · pdf · doi:10.48550/arxiv.2506.06932

Abstract

We propose a conjecture on the p-adic nowhere density of the Hecke orbit of subvarieties of Hodge type Shimura varieties. By investigating the monodromy of p-adic Galois representations associated with points on such Shimura varieties, we prove that the locus in a formal O_K-neighborhood of a mod p point that has large monodromy is open dense, where K is a totally ramified finite extension of \breveℚ_p.

Citations

• Abelian varieties are not quotients of low-dimension Jacobians
• On the connectedness of p-adic period domains
• The connected components of affine Deligne–Lusztig varieties
• Hecke orbits on Shimura varieties of Hodge type
• On the geometric connected components of moduli spaces of p-adic shtukas and local Shimura varieties
• Towards a theory of local Shimura varieties
• Rapoport-Zink spaces of Hodge type
• Good Reductions of Shimura Varieties of Hodge Type in Arbitrary Unramified Mixed Characteristic, Part II
• Integral Canonical Models of Shimura Varieties of Preabelian Type
• Subvarieties of Shimura varieties

Related

• Hecke orbits on Shimura varieties of Hodge type
• On The Hecke Orbit Conjecture for PEL Type Shimura Varieties
• p-adic monodromy and mod p unlikely intersections, I
• Subvarieties of Shimura varieties
• Height functions on Hecke orbits and the generalised André-Pink-Zannier conjecture