标题： 经典的psh和Berkovich空间上的全纯函数 显示英文标题

标题： Classically psh and pluriharmonic functions on Berkovich spaces

摘要： 首先，我们将Thuillier学位论文中关于光滑严格$k$-解析曲线上的次调和函数理论推广到可能具有奇异性的非阿基米德域上的解析曲线的情形。 经典地，正位势（psh）函数通过将函数拉回到解析曲线来定义（并要求与基变换兼容）。我们给出了经典psh函数的若干性质，包括局部最大值原理和全局最大值原理。 由此得出结论，在拟紧致Berkovich空间上全调和函数的空间是有限维的。 作为技术工具，我们利用了连通的Berkovich空间可以通过解析曲线连接这一事实。 显示英文摘要

摘要： First we extend the theory of subharmonic functions on smooth strictly $k$-analytic curves from Thuillier's thesis to the case of possibly singular analytic curves over a non-archimedean field. Classically psh functions are then defined as in complex geometry by using pullbacks to analytic curves (and requiring compatibility with base change). We give various properties of classically psh functions including a local and a global maximum principle. As a consequence, we show that the space of pluriharmonic functions on a quasi-compact Berkovich space is finite dimensional. As a technical tool, we use that a connected Berkovich space is connected by analytic curves.