Differentiability of the χ-volume function over an adelic curve

2023/03/06 by Sédillot, Antoine
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2303.03377

Abstract

In this article, we show a differentiability property for the χ-volume function on the ample cone of adelic line bundles over an adelic curve. This result is deduced from a non-Archimedean counterpart of a diffrentiability result of Witt Nyström. As an application, we give a logarithmic equidistribution result over adelic curves.

Related

• The continuity of χ-volume functions over adelic curves
• Continuous Extension and Birational Invariance of χ-Volume Over an Adelic Curve
• Differentiability of Adelic Volumes and Equidistribution on Quasi-Projective Varieties
• Differentiability of relative volumes over an arbitrary non-Archimedean field
• Differentiability of the arithmetic volume function along the base conditions