Special Cycles on Toroidal Compactifications of Orthogonal Shimura Varieties

2019/12/26 by Bruinier, Jan Hendrik, Zemel, Shaul · 1 citation
#11F27 #14G35 #14M27 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1912.11825

Abstract

We determine the behavior of automorphic Green functions along the boundary components of toroidal compactifications of orthogonal Shimura varieties. We use this analysis to define boundary components of special divisors and prove that the generating series of the resulting special divisors on a toroidal compactification is modular.

Cited by

• The cohomological Kudla conjecture for unitary Shimura varieties

Related

• Modularity of special 0-cycles on toroidal compactifications of Shimura Varieties
• Mixed mock modularity of special divisors
• Derived special cycles on Shimura varieties
• Complex multiplication cycles and Kudla-Rapoport divisors II
• Generating series of intersection volumes of special cycles on unitary Shimura varieties