Connected components of special cycles on Shimura varieties

2025/05/04 by Madapusi, Keerthi
#11S99 #14F30 #14L05 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2505.02084

Abstract

I use methods of Chai-Hida and ordinary p-Hecke correspondences to study the set of irreducible components of special fibers of special cycles of sufficiently low codimension in integral models of GSpin Shimura varieties, and apply this to prove irreducibility results for the special fibers of the moduli of polarized K3 surfaces. These results are also applied in joint work with Howard on the modularity of generating series of higher codimension cycles on GSpin Shimura varieties.

Citations

• Monodromy and Irreducibility of Igusa Varieties
• Arithmetic of Borcherds products
• Serre-Tate theory for Shimura varieties of Hodge type
• Faltings heights of abelian varieties with complex multiplication
• Height pairings on orthogonal Shimura varieties
• The Tate conjecture for K3 surfaces in odd characteristic
• Integral canonical models for Spin Shimura varieties
• Toroidal compactifications of integral models of Shimura varieties of\n Hodge type
• Algebraic Groups Over Finite Fields

Related

• Derived special cycles on Shimura varieties
• Cycles on Shimura varieties via geometric Satake
• The Tate conjecture for K3 surfaces in odd characteristic
• Integral canonical models for Spin Shimura varieties
• A note about special cycles on moduli spaces of K3 surfaces