Arithmetic of Borcherds products
Benjamin Howard, Keerthi Madapusi Pera
TL;DR
This paper computes divisors of Borcherds products on orthogonal Shimura varieties and establishes an integral version of Borcherds' modularity theorem for special divisors.
Contribution
It provides the first integral model computation of Borcherds products' divisors and extends Borcherds' modularity results to integral settings.
Findings
Divisors of Borcherds products on integral models are explicitly computed.
An integral version of Borcherds' modularity theorem is established.
Enhanced understanding of special divisors in integral models of Shimura varieties.
Abstract
We compute the divisors of Borcherds products on integral models of orthogonal Shimura varieties. As an application, we obtain an integral version of a theorem of Borcherds on the modularity of a generating series of special divisors.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Advanced Topics in Algebra · Algebraic Geometry and Number Theory