Timeline for Are the unipotent and nilpotent varieties isomorphic in bad characteristics?
Current License: CC BY-SA 4.0
8 events
when toggle format | what | by | license | comment | |
---|---|---|---|---|---|
Feb 21, 2022 at 14:00 | history | edited | LSpice | CC BY-SA 4.0 |
Links while this is on the front page
|
May 5, 2017 at 1:41 | history | edited | George McNinch | CC BY-SA 3.0 |
added 962 characters in body
|
May 5, 2017 at 0:50 | comment | added | George McNinch | @Paul: Indeed, "zero locus of the positive degree invariants" is surely what I should have intended. | |
May 4, 2017 at 21:31 | comment | added | Paul Levy | I checked in Magma and the nullcone of $\mathfrak{sp}_4$ in characteristic 2 is reduced... | |
May 4, 2017 at 21:19 | comment | added | Paul Levy | By the scheme of nilpotent elements, I assume you mean the zero locus of the set of homogeneous invariants of positive degree. But in characteristic 2 I don't think the ring of invariants is known in general, which would suggest that your question is quite non-trivial. Incidentally, I am fairly sure one can show that the nullcone of $\mathfrak{pgl}_n$ is non-reduced at the subregular locus for arbitrary $n$. | |
May 4, 2017 at 17:05 | comment | added | George McNinch | Maybe a first question is: if $G$ is simply connected case, are the "scheme of unipotent elements" and the "scheme of nilpotent elements" reduced? | |
May 4, 2017 at 14:34 | comment | added | Jim Humphreys | This does get complicated, but I'm asking mainly about simply connected groups $G$ for bad $p$ (as in Springer's theorem for good $p$). Your discussion illustrates the extra obstacles when $G$ isn't simply connected. [By the way, I'd expect similar phenomena for adjoint groups of type $A_\ell$ whenever $p | (\ell+1)$, though of course it's hard to be as concrete as in the case $\ell =1$.] | |
May 4, 2017 at 12:29 | history | answered | George McNinch | CC BY-SA 3.0 |