演講摘要 : Berkovich geometry was established by V. G. Berkovich in 1990 to introduce analytic techniques into algebraic geometry over arbitrary fields.
Historically, this was not the first attempt. In 1961, J. Tate had already established such a theory over non-Archimedean fields, which is known as rigid geometry.
However, Berkovich geometry has many great features that are absent in rigid geometry. One of them is its high affinity with complex geometry.
In this talk, I'll briefly explain this feature by introducing basic results in Berkovich geometry.
If time permits, I'll also explain my previous works related to it.