Introduction to Affine Group Schemes

The purpose of the course is to introduce affine group schemes via the functor of points approach. It was a 4-weekly-hours one-semester course. By the end of the course, we proved two main results: every affine group scheme of finite type over a field is linear, and the classification of representations of G_m over a field.

This course was a pilot, and I think that next time I will teach it, I will rearrange the chapter about affine schemes to include the changes introduced in the lecture titled "Affine Group Schemes C", and might also include a discussion of the topological space underlying an affine scheme. I nevertheless put the notes here in case they are useful to anyone. In the missing introductory lecture I introduced group schemes informally as groups which are solutions of a system of polynomial equations etc., gave examples, hinted that we are dealing with functors, and stated (somewhat vaguely) the classification of simple algebraic groups over an algebraically closed field.

Lecture notes (in Hebrew)

• Introductory lecture. No notes unfortunately.
• Algebras A. No notes unfortunately. The subject was modules over commutative rings, including free modules.
• Algebras B
• Categories A
• Categories B
• Categories C
• Categories D
• Categories E
• Affine Schemes A
• Affine Schemes B
• Affine Schemes C
• Affine Schemes D
• Affine Schemes E
• Affine Schemes F
• Affine Schemes G
• Tensor Products A
• Tensor Products B
• Tensor Products C
• Tensor Products D
• Tensor Products E
• Tensor Products F + Affine Group Schemes A
• Affine Group Schemes B
• Affine Group Schemes C
• Affine Group Schemes D
• Affine Group Schemes E + Representations A
• Representations B
• Representations C
• Representations D
• Representations E
• Representations F