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20 votes
7 answers
9k views

Elementary reference for algebraic groups

I'm looking for a reference on algebraic groups which requires only knowledge of basic material on the theory of varieties which you could find in, for example, Basic Algebraic Geometry 1 by ...
David Corwin's user avatar
  • 15.4k
26 votes
1 answer
2k views

Example of non-projective variety with non-semisimple Frobenius action on etale cohomology?

This question was motivated by a more general question raised by Jan Weidner here. In general one starts with a variety $X$ (say smooth) over an algebraic closure of a finite field $\mathbb{F}_q$ of ...
Jim Humphreys's user avatar
14 votes
2 answers
3k views

How many ways are there to prove flag variety is a projective variety?

I am looking for references talking about different ways to prove flag variety $G/B$ is projective variety. Now I have some in mind: There is a proof in Humphreys Linear algebraic groups, he first ...
Shizhuo Zhang's user avatar
3 votes
2 answers
654 views

Simple representations of products of algebraic groups

I am looking for a reference for the following assertion that I believe to be true. All representations are assumed to be finite-dimensional. Let $G_1$ and $G_2$ be affine algebraic group schemes ...
Communicative Algebra's user avatar