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Fakultät für Mathematik Universität Regensburg
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Non-Archimedean Analytic Geometry
Semester
WiSe 2025 / 26

Lecturer
Klaus Künnemann

Type of course (Veranstaltungsart)
Vorlesung

German title
Non-Archimedean Analytic Geometry

Contents
This course gives an introduction to non-archimedean analytic geometry. We present the approach by
Berkovich developed in his book 'Spectral theory and analytic geometry over non-archimedean fields'
and subsequent papers. We will study affinoid analytic spaces and introduce general non-archimedean
analytic spaces. If time permits, we will discuss also non-archimedean analytifications of algebraic
varieties, tropicalizations and non-archimedean analytic curves. This course will assume familiarity
with the material from the course on Non-Archimedean Banach Algebras that I have taught in the
summer term 2025. Course notes of this course are available. If you want to attend this course and
you have not attended my course on Non-Archimedean Banach Algebras, then it is recommended that you
participate in the seminar on Non-Archimedean Banach Algebras that I organize in the winter term
2025/26 in parallel. Participants of this course will profit from some familiarity with algebraic
geometry that can be obtained by attending the course on Algebraic Geometry by Marc Hoyois in
parallel.

Time/Date
Monday, Thursday 8h15-10h00

Location
M104

Registration
  • Registration for course work/examination/ECTS: FlexNow
Course work (Studienleistungen)
  • Successful participation in the exercise classes:
Examination (Prüfungsleistungen)
  • Oral exam: Duration: 30 minutes, Date: by individual appointment, re-exam: Date: by individual
    appointment
Modules
BV, MV, MArGeo

ECTS
9 LP
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