346 reputation
18
bio website rupertmccallum.com
location Germany
age 38
visits member for 3 years, 4 months
seen yesterday
I am doing a post-doctoral research position about topological buildings and topological groups at the University of M√ľnster.

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?