Arithmetic Volumes of Unitary Shimura Varieties
Abstract
The integral model of a G U ( n − 1 , 1 ) \mathrm {GU}(n-1,1) Shimura variety carries a universal abelian scheme over it, and the dual top exterior power of its Lie algebra carries a natural hermitian metric. We express the arithmetic volume of this metrized line bundle, defined as an iterated self-intersection in the arithmetic Chow ring, in terms of logarithmic derivatives of Dirichlet L L -functions. We also determine the arithmetic volumes of Kudla-Rapoport divisors and relate them to coefficients of Eisenstein series.
Fields of Study & Subjects
Advanced Algebra and Geometry
Algebraic Geometry and Number Theory
Advanced Mathematical Identities
Publication details
- Journal / source
- Memoirs of the American Mathematical Society
- Publisher
- American Mathematical Society (AMS)
- Volume
- 318
- Issue
- 1619
- Publication date
- 27 February 2026
- Language
- EN