Adelic Cartier divisors with base conditions and the continuity of volumes
arXiv:1702.03514 · doi:10.1215/21562261-2021-0018
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.
36 pages