Introduction to Berkovich Geometry

If students who do not speak German want to participate, the class will be held in English. Else we can speak German. Of course, questions can be asked in German any time!

If you have questions about the class, please contact Felix Röhrle.

The class takes place Tuesday 14:00 -- 16:00 NEW TIMESLOT: Tuesday 16:00 -- 18:00 in room C2A17. Registration is not necessary. There are no exercise classes.

Requirements for this class are: Analysis 1+2, Linear Algebra 1, Algebraic structures, and some experience with topology. Any prior knowledge of algebraic geometry is helpful but not necessary. The lecture will be adjusted depending on the audience.

The topics include: non-Archimedean fields, the Berkovich affine line, and the analytification functor. The geometric objects discussed in this class are wildly different from varieties or manifolds and will introduce you to a theory where the analogue of a straight line is an infinitely self-similar fractal.

The class will follow at least in the beginning the following notes (in German, references to material in English can be provided).

There will be oral exams in the next term-free time.

Notes on field of Laurent series: pdf.

Berkovich unit disc for trivially valued base field: pdf.