Institut de Géométrie, Algèbre et Topologie
Workshop on Tannakian Categories
12 - 16 July 2010
BCH 2103
Organizers: Kathryn Hess and Peter Jossen
Introduction
A neutral Tannakian category is a special kind of monoidal category, together with extra
structure relative to a field k. The Main Theorem in Tannakian theory states that every Tannakian category is equivalent to the category of
finite dimensional k-representations of a group scheme,
which is unique up to isomorphism. Historically, the theory of Tannakian categories generalizes
Tannaka-Krein duality for compact topological groups.
In this workshop we will survey the theory of Tannakian categories, starting from basic notions in category theory. We will prove the Main Theorem and
see numerous interesting examples. We will also explore the relationship between Tannakian theory and Galois theory.
For a more complete introduction to the workshop, including a description of the subjects of the individual talks, please click here.
The format of this workshop is modeled on that of the Arbeitsgemeinschaften of Oberwolfach, so that most workshop participants will give at least one talk.
EPFL doctoral students will receive one credit for participating in the workshop and giving a talk.
Potential participants should contact Kathryn Hess as soon as possible, indicating which, if any, of the talks they would be willing to give.
The more participants the merrier!
Program
| Date/Time | Title | Speaker |
|---|---|---|
Monday 9:00 |
Introduction |
Peter Jossen Regensburg |
Monday 10:30 |
Tensor categories and tensor functors | Rosalie Chevalley EPFL |
Monday 14:00 |
Abelian and linear tensor categories | Alex Monnard EPFL |
Monday 15:30 |
Tannakian categories | Dimitri Zaganidis EPFL |
Tuesday 9:00 |
Affine schemes and the functor of points | Lev Kiwi EPFL |
Tuesday 10:30 |
Affine group schemes and algebras | Matteo Paganin EPFL |
Tuesday 14:00 |
Representations and comodules | Steve Bennoun UBC |
Tuesday 15:30 |
Categories of finite dimensional representations are Tannakian | Fabio Trova Padova/EPFL |
Wednesday 9:00 |
Recovering a group scheme from its representations | Caroline Lassueur EPFL |
Wednesday 10:30 |
The Main Theorem | Gavin Seal EPFL |
Wednesday 14:00 |
Proof of the Main Theorem I | Marc Hoyois Northwestern |
Wednesday 15:30 |
Proof of the Main Theorem II | Marc Hoyois Northwestern |
Thursday 9:00 |
Example I: Graded vector spaces | Varvara Karpova EPFL |
Thursday 10:30 |
Example II: Fibre bundles and fundamental groups | Jérôme Scherer EPFL |
Thursday 14:00 |
Example III: Galois groups | Kathryn Hess EPFL |
Thursday 15:30 |
Example IV: Hodge structures | Giorgio Trentinaglia Göttingen |
Friday 9:00 |
Galois theory à la Grothendieck | Peter Jossen Regensburg |
Friday 10:30 |
Galois groups and fundamental groups | Peter Jossen Regensburg |
Friday 14:00 |
Tannaka duality for comonoids | Daniel Schäppi Chicago |
P. Deligne, Tannakian Categories, Lecture Notes in Matematics 100, Springer, 1980.
D. Schäppi, Tannaka duality for comonoids in cosmoi.
T. Szamuely, Galois Groups and Fundamental Groups, Cambridge Studies in Adv. Math. 117, Cambridge University Press, 2009.
W.C. Waterhouse, Introduction to Affine Group Schemes, Graduate Texts in Mathematics 66, Springer, 1979.
Tannaka Duality, nLab.
