# Adelic Cartier divisors with base conditions and the continuity of volumes

## TL;DR

This paper extends the concept of adelic R-Cartier divisors to l1-adelic R-Cartier divisors and proves the continuity of the associated arithmetic volume function in this broader setting.

## Contribution

It introduces l1-adelic R-Cartier divisors and establishes the continuity of the volume function on this extended space.

## Key findings

- Introduction of l1-adelic R-Cartier divisors
- Proof of volume function continuity in the new setting
- Extension of previous notions to broader classes

## Abstract

In the previous paper [7], we introduced a notion of pairs of adelic R-Cartier divisors and R-base conditions. The purpose of this paper is to propose an extended notion of adelic R-Cartier divisors that we call an l1-adelic R-Cartier divisors, and to show that the arithmetic volume function defined on the space of pairs of l1-adelic R-Cartier divisors and R-base conditions is continuous along the directions of l1-adelic R-Cartier divisors.