Modularity of special cycles on Shimura varieties: a survey

arXiv (Cornell University) 2026 Preprint Open access

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Authors: François Greer, Salim Tayou
DOI: 10.48550/arxiv.2603.01251
Cited by: 0
References: 8

Abstract

We survey recent results on a conjecture of Kudla regarding the modularity of generating series of special cycle classes in toroidal compactifications of orthogonal and unitary Shimura varieties. Along the way, we formulate several conjectures on related phenomena for special cycles in other types of Shimura varieties, as well as on more general quotients of period domains.

Fields of Study & Subjects

Advanced Algebra and Geometry Algebraic Geometry and Number Theory Advanced Mathematical Identities

Publication details

Journal / source
arXiv (Cornell University)
Publication date
1 March 2026
Language
EN
Document type
Preprint