Modularity of generating series of divisors on unitary Shimura varieties

2017/02/25 by Jan Hendrik Bruinier, Bruinier, Jan, Benjamin Howard +7 · 2 citations
Chemistry · Mathematics · #11F27 #11F55 #14G35 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Molecular spectroscopy and chirality #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1702.07812

openalex publication_date 2017/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We form generating series of special divisors, valued in the Chow group and in the arithmetic Chow group, on the compactified integral model of a Shimura variety associated to a unitary group of signature (n-1,1), and prove their modularity. The main ingredient of the proof is the calculation of the vertical components appearing in the divisor of a Borcherds product on the integral model.

Cited by

• Positive density of primes of ordinary reduction for abelian varieties of simple signature
• The cohomological Kudla conjecture for unitary Shimura varieties

Related

• Arithmetic of Borcherds products
• Modularity of arithmetic special divisors for unitary Shimura varieties (with an appendix by Yujie Xu)
• Modularity of generating series of divisors on unitary Shimura varieties II: arithmetic applications
• Modular Heights of Unitary Shimura Varieties I: Derivatives of Eisenstein Series
• Mixed mock modularity of special divisors