Manitori

The note is mainly a sketch of basic knowledge concerning general topology, differential geometry, functional analysis, algebraic geometry, etc., starting from a discussion of Euclidean spaces. However, there maybe some mistakes in the note, so use at your own risk. For simplicity, some details are omitted and can be found in the references provided. Further materials concerning algebraic geometry, especially arithmetic algebraic geometry, can be referred to another note written by the author, N ...

The note is mainly a summary of basic knowledge that the author learned in arithmetic geometry. One of the aims of this note is to provide a preliminary for Perfectoid geometry. Most contents are fundamental, but they are essential towards Perfectoid geometry. The ultimate goal of this note is to help readers to understand Peter Scholze's classic paper , where the notion of perfectoid spaces first appeared.