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## Linear Algebraic Groups | SpringerLink

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## 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?

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