Issues About Advertising and Corporate Services.

- Red Meat Cures Cancer.
- Advanced Studies in Pure Mathematics.
- Providence: The Story of a Fifty-Year Vision Quest;

Advanced Search. Article Navigation.

### Navigation menu

Close mobile search navigation Article Navigation. Volume Oxford Academic. Google Scholar. Cite Citation. Article PDF first page preview.

## Linear Algebraic Groups | SpringerLink

Issue Section:. You do not currently have access to this article. Download all figures. Sign in. You could not be signed in.

Sign In Forgot password? Don't have an account?

## Endomorphisms of linear algebraic groups

Sign in via your Institution Sign in. This article is also available for rental through DeepDyve. In particular:. Here G is a connected simple algebraic group over an algebraically closed field, essentially treated as a group scheme. That seems to be a good setting for the question I've raised, though perhaps one can go further in the direction of reductive groups?

ADDED: The answers and comments are very interesting, but while I think further about them and the literature I should clarify that I'm taking for granted the standard though nontrivial formulas for the group orders over finite fields.

## On the computation of conjugacy classes of Chevalley groups

And while it's natural at least for Chevalley groups to start over the ring of integers, there is certainly a passage to local rings implied here. The specific prime stays in the background, since unlike many questions in Lie theory this kind of computation doesn't distinguish "good" and "bad" primes: whatever is done should apply uniformly to all primes. Meanwhile a result in Appendix A. This suggests that groups aren't so essential to my question, but only a well-behaved class of schemes again assuming that one can already count their points over finite fields. The result in Demazure-Gabriel to which Serre refers in the article "Exemples de plongements Remarks: 1 It seems to me?

It would be very interesting to know if any progress has been made on this since Greenberg's paper appeared. Edit: It may not be necessary to go via Greenberg's conjecture.

The point-count over finite fields is related to the action of Frobenius on the twisted dual motive: equation 3. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Uniform setting for computing orders of algebraic groups over finite quotients of the integers?

- Plural Predication!
- Additive polynomials for finite groups of Lie type.
- The Unforgotten Sisters: Female Astronomers and Scientists before Caroline Herschel?
- The Antinomies of Realism.
- Organic Syntheses , Volume 77.
- Download Endomorphisms Of Linear Algebraic Groups: Number 80?
- Subscribe to RSS?
- Endomorphisms of Linear Algebraic Groups.
- Science and Skiing.
- Conjugacy classes!
- The Science Fiction Book: An Illustrated History!
- Download Endomorphisms Of Linear Algebraic Groups: Number 80?
- The Limits of Morality.

Ask Question. Asked 7 years, 7 months ago. Active 7 years, 7 months ago. Viewed times.

Jim Humphreys Jim Humphreys