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Fakultät für Mathematik Universität Regensburg
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Motivic homotopy theory
Semester
WiSe 2026 / 27

Lecturer
Marc Hoyois

Type of course (Veranstaltungsart)
Vorlesung

German title
Motivische Homotopietheorie

Contents

Motivic homotopy theory was developed by F. Morel and V. Voevodsky in the late 90s in order to "do homotopy theory" with schemes. This course will introduce motivic homotopy theory from a modern perspective. Topics will include:

  • Categorical preliminaries (presentable categories, Bousfield localization, sheaves)
  • Algebro-geometric preliminaries (smoothness, blowups, the tubular neighborhood theorem)
  • The purity and localization theorems
  • Geometric models for classifying spaces
  • The A¹-homotopical classification of vector bundle
  • Motivic spectra and the stable A¹-connectivity theorem
  • Examples: algebraic K-theory, hermitian K-theory, motivic cohomology
  • Oriented cohomology theories and algebraic cobordism
  • The six-functor formalism


Recommended previous knowledge
Familiarity with category theory and with schemes is assumed, but some of the necessary background (including higher category theory) will be reviewed at the beginning of the course.

Time/Date
Wed, Thu 8-10

Location
M102

Additional question session
Time/Date: Wed 10-12
Location: tbd

Course homepage
https://hoyois.app.uni-regensburg.de/WS27/mht/index.html
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)

Registration
  • Registration for course work/examination/ECTS: FlexNow
Course work (Studienleistungen)
  • Successful participation in the exercise classes:
Examination (Prüfungsleistungen)
  • Oral exam: Duration: 25 minutes, Date: by appointment, re-exam: Date: by appointment
Modules
BV, MV, MArGeo, MGAGeo

ECTS
9
Druckansicht