Avsnittsöversikt
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Schedule:
The first lecture will be on Monday the 19th of January 10h-12h in Cramer room (Albano House 1, Floor 3). We will decide the regular schedule that suits you best then. There will be 14 lectures of 2 hours.
Teachers:
Marion Jeannin (marion.jeannin@math.su.se)
Examination:
Four problem sheets will be distributed. To pass, you need to obtain 1/4 of the score on each problem sheet, and 1/2 of the total score.
Prerequisites:
Abstract algebra and topology. A good knowledge in commutative algebra, classical algebraic geometry and category theory would be helpful but not compulsory.
Contents:
The aim of the course is to develop the theory of affine group schemes over rings from the basics and conclude with the structure theory of reductive group schemes.
Lecture plan Lecture 1 Lecture 2 Lecture 3 Lecture 4 Lecture 5 Lecture 6 Lecture 7 Lecture 8 Lecture 9 Lecture 10 Lecture 11 Lecture 12 Lecture 13 Lecture 14 Literature:
The topics of the course are largely covered in:
- [C] B. Conrad, Reductive group schemes
- [G] P. Gille, Introduction to reductive group schemes over rings.
- [V] A. Vistoli, Notes on Grothendieck topologies, fibered categories and descent theory.
A good algebraic introduction to affine group schemes can also be found in Introduction to Affine Group Schemes by Waterhouse. The basic reference is the (hard-to-find) book Groupes algébriques by Demazure and Gabriel. For Grothendieck topologies, another reference is Introduction to étale cohomology by Günter Tamme.