论文标题
在任意非架构场上的相对体积的不同性
Differentiability of relative volumes over an arbitrary non-Archimedean field
论文作者
论文摘要
考虑到在任意非架构的非架构领域定义的几何降低的投射方案上有足够的线条束$ L $，我们在$ L $的Berkovich分析上为两个连续指标的相对体积建立了一个可不同的属性，从而扩展了以前已知的结果，以延长了离散估值的情况。作为应用程序，我们为某些非Archimedean Monge和Ampère方程提供了基本解决方案，并概括了Fekete点的等分分配结果。我们的主要技术输入来自共同体和deligne配对的决定因素。
Given an ample line bundle $L$ on a geometrically reduced projective scheme defined over an arbitrary non-Archimedean field, we establish a differentiability property for the relative volume of two continuous metrics on the Berkovich analytification of $L$, extending previously known results in the discretely valued case. As applications, we provide fundamental solutions to certain non-Archimedean Monge--Ampère equations, and generalize an equidistribution result for Fekete points. Our main technical input comes from determinant of cohomology and Deligne pairings.
