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Selected topics in algebraic geometry I - 2025 Spring 1

I am teaching a half-semester course at ISTA on basics of Tannakian formalism.
We will roughly follow [DM, Chapters 1-3] and [Sza, Chapter 6], complemented by further examples and applications.

The lecture will take place on Wednesdays at 13:00-16:00 (with a break) in the Heinzel seminar room (I21.EG.101).
Here is a link to the internal course page in Athena. The first lecture takes place on March 5.

Schedule:
Wed 5.3.: Motivation; covering spaces; separable field extensions. Affine group schemes and commutative Hopf algebras.
Wed 12.3.: Algebraic representations; coalgebras and comodules. Representations of the additive and multiplicative groups over fields.
Wed 19.3.: Reconstruction of coalgebras.
Wed 26.3.: Tensor categories; rigidity.
Wed 2.4.: Algebraic Tannaka-Krein theorem. Neutral Tannakian categories; main theorem of Tannakian formalism.
Wed 9.4.: ---
---: participant presentations

Literature:
[DM] Deligne, Milne: Tannakian categories
[Sza] Szamuely: Galois groups and fundamental groups
[Mil] Milne: Algebraic groups
[EGNO] Etingof, Gelaki, Nikshych, Ostrik: Tensor categories
[CW] Ciappara, Williamson: Lectures on the geometry and modular representation theory of algebraic groups
[SR] Saavedra Rivano: Catégories tannakiennes