Arithmetic volumes of unitary Shimura curves

TL;DR

This paper calculates the arithmetic volumes of integral models of unitary Shimura curves, providing a foundational step for future work on higher-dimensional cases of unitary Shimura varieties.

Contribution

It introduces a method to compute arithmetic volumes of unitary Shimura curves, serving as the base case for an inductive approach to higher-dimensional varieties.

Findings

Arithmetic volumes of integral models of unitary Shimura curves are computed.

Establishes a base case for inductive calculations of higher-dimensional unitary Shimura varieties.

Supports future research in the arithmetic geometry of Shimura varieties.

Abstract

We compute the arithmetic volumes of integral models of unitary Shimura curves. This establishes the base case of an inductive argument to compute the arithmetic volumes of unitary Shimura varieties of higher dimension, to appear in subsequent work of Bruinier and the author.