学术报告（蔡毓麟 6.29）

Abstract: One principle in number theory is that all completions of a global field should be treated in a symmetric way, i.e. $\Q_p$ and $\R$ play equal roles. However, the classical Arakelov theory seems to violate this principle: we consider the non-archimedean part with regular models and archimedean part with analytic geometry. The theory of Berkovich spaces is a version of analytic geometry over non-archimedean field. It has been applied to Arakelov theory since the work of Chinburg-Rumely and Zhang. In this talk, we will introduce δ-forms on Berkovich spaces, which extends the ones given by Gubler-Künnemann, and explain how they are used in Arakelov theory.

数论的一个原则是，整体域的所有完备化都应以对称的方式处理，即$\Q_p$和$\R$扮演着平等的角色。然而，经典的Arakelov理论似乎违反了这一原则：我们分别考虑具有正则模型的非阿基米德部分和具有解析几何的阿基米德部分。Berkovich空间理论是非阿基米德域上解析几何的一个版本。自Chinburg-Rumely和Zhang工作以来，它一直应用于Arakelov理论。在这次报告中，我们将介绍Berkovich空间上的δ形式，它扩展了Gubler-Künnemann给出的δ形式，并解释它们在Arakelov理论中的使用方式。