Universität Regensburg   IMPRESSUM   DATENSCHUTZ
Fakultät für Mathematik Universität Regensburg

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English Note For our digital courses all relevant information can be found on the appropriate GRIPS sites.

Perfectoid Spaces
Semester
SoSe 2021

Lecturer
Walter Gubler

Type of course (Veranstaltungsart)
Vorlesung

Contents
The main goal of this course is to develop the basic theory of perfectoid spaces. We will focus
mainly on perfectoid algebras, the affine part for adic spaces and the language of almost
mathematics. Perfectoid spaces have been introduced by Peter Scholze as a tool to transport
problems in arithmetic geometry from characteristic 0 to characteristic p where they are sometimes
easier to solve thanks to the Frobenius morphism. These perfectoid methods already have several
spectacular applications in different areas of mathematics, e.g. in commutative algebra, algebraic
geometry, and p-adic Hodge theory.

Recommended previous knowledge
Algebra. Knowledge from Algebraic Number Theory is not required, but for those who attended, it
would be a natural continuation.

Time/Date
Tuesday, Thursday 8--10

Location
Zoom (provisionally)

Registration
  • Registration for the exercise classes: GRIPS
  • Registration for course work/examination/ECTS: FlexNow
Course work (Studienleistungen)
  • Successful participation in the exercise classes: 50% of the exercise points.
Examination (Prüfungsleistungen)
  • Oral exam: Duration: 25 minutes, Date: TBA, re-exam: Date: TBA
Regelungen bei Studienbeginn vor WS 2015 / 16
  • Benotet:
    • O. g. Studienleistung und o. g. Prüfungsleistung; die Note ergibt sich aus der Prüfungsleistung
  • Unbenotet:
    • O. g. Studienleistung
Modules
BV, MV, MArGeo

ECTS
9