bio | website | rupertmccallum.com |
---|---|---|
location | Germany | |
age | 38 | |
visits | member for | 3 years, 4 months |
seen | yesterday | |
stats | profile views | 163 |
I am doing a post-doctoral research position about topological buildings and topological groups at the University of Münster.
Oct 14 |
comment |
pro-Lie-groups and the exponential map
Okay, thanks, is it true to say that a nontrivial pro-Lie group always has a subgroup which is abstractly isomorphic to a one-dimensional Lie group, or not? |
Oct 13 |
asked | pro-Lie-groups and the exponential map |
Oct 13 |
accepted | the meaning of “Cauchy filter” for an arbitrary topological group |
Oct 13 |
asked | the meaning of “Cauchy filter” for an arbitrary topological group |
Oct 2 |
accepted | algebraic groups over non-archimedean local fields acting on buildings |
Oct 2 |
asked | algebraic groups over non-archimedean local fields acting on buildings |
Sep 22 |
comment |
query about quasi-simple algebraic groups over local fields
There is a result due to Nikolov and Segal that could be relevant. arxiv.org/abs/1102.3037 They show that a finitely generated profinite group has a countably infinite abstract quotient if and only if it has an infinite virtually abelian continuous quotient. |
Sep 22 |
comment |
query about quasi-simple algebraic groups over local fields
Thank you. May I ask, is it also possible to rule out the possibility that an open compact subgroup of such a group could have a countably infinite abstract quotient? |
Sep 22 |
accepted | query about quasi-simple algebraic groups over local fields |
Sep 22 |
comment |
query about quasi-simple algebraic groups over local fields
I was trying to prove that the group of rational points of every absolutely quasi-simple algebraic group over a non-archimedean local field had a rigid topology. The reviewer found my argument unsatisfactory in the positive-characteristic case but suggested that I work on the more general problem of trying to prove topological rigidity for totally disconnected locally compact $\sigma$-compact groups which are locally finitely generated and locally hereditarily just infinite. I am interested in clarifying whether the first question is indeed a special case of the second. |
Sep 22 |
asked | query about quasi-simple algebraic groups over local fields |
Aug 26 |
awarded | Popular Question |
Jul 2 |
awarded | Curious |
May 26 |
comment |
when the derived group of the group of $k$-rational points has nonempty interior in the strong topology
Many thanks for your help. Peter McNamara, can I ask you to elaborate further about the anisotropic case. I was told that the only examples of anisotropic absolutely quasi-simple algebraic groups over local fields of positive characteristic were of the form $\mathrm{SL}_{1}(\Delta)$ for central simple division algebras $\Delta$, and that the derived group $[G(k),G(k)]$ was equal to the group of norm-1 units in the unique maximal order of $\Delta$, which I thought was open in the strong topology? Does this include your anisotropic form of $\mathrm{PGL_p}$? |
May 26 |
accepted | when the derived group of the group of $k$-rational points has nonempty interior in the strong topology |
May 19 |
comment |
when the derived group of the group of $k$-rational points has nonempty interior in the strong topology
Many thanks for your help. Yes, strong topology does mean the topology coming from the topology on $k$. I think I heard that phrase used somewhere in an algebraic geometry textbook but I'm not sure. Do you know of anywhere where I can read more about the Steinberg presentation? |
May 15 |
asked | when the derived group of the group of $k$-rational points has nonempty interior in the strong topology |
May 8 |
accepted | an algebraic group where the function field is not separable over the ground field |
May 7 |
asked | an algebraic group where the function field is not separable over the ground field |
May 7 |
accepted | A strengthened version of Noether's normalisation lemma? |