scholarly journals On Galois cohomology of unipotent algebraic groups over local fields

2011 ◽  
Vol 344 (1) ◽  
pp. 47-59
Author(s):  
Nguyêñ Duy Tân
Keyword(s):  
Algebraic Groups ◽  
Galois Cohomology ◽  
Local Fields ◽  
Unipotent Algebraic Groups

Galois Cohomology of Unipotent Algebraic Groups and Field Extensions

2011 ◽  
Vol 39 (11) ◽  
pp. 3923-3938 ◽  
Author(s):  
Nguyêñ Duy Tân ◽  
Nguyêñ Quôć Thǎńg
Keyword(s):  
Algebraic Groups ◽  
Galois Cohomology ◽  
Field Extensions ◽  
Unipotent Algebraic Groups

scholarly journals Random groups and nonarchimedean lattices

2014 ◽  
Vol 2 ◽  
Author(s):  
SYLVAIN BARRÉ ◽  
MIKAËL PICHOT
Keyword(s):  
Algebraic Groups ◽  
Local Fields ◽  
Density Model ◽  
Rank 2 ◽  
Higher Rank ◽  
Random Groups

AbstractWe consider models of random groups in which the typical group is of intermediate rank (in particular, it is not hyperbolic). These models are parallel to Gromov’s well-known constructions, and include for example a ‘density model’ for groups of intermediate rank. The main novelty is the higher rank nature of the random groups. They are randomizations of certain families of lattices in algebraic groups (of rank 2) over local fields.

scholarly journals CHABAUTY LIMITS OF ALGEBRAIC GROUPS ACTING ON TREES THE QUASI-SPLIT CASE

2018 ◽  
Vol 19 (4) ◽  
pp. 1031-1091
Author(s):  
Thierry Stulemeijer
Keyword(s):  
Algebraic Group ◽  
Closed Subset ◽  
Algebraic Groups ◽  
Local Fields ◽  
Locally Finite ◽  
Simple Algebraic Group ◽  
Groups Acting On Trees ◽  
Residue Characteristic

Given a locally finite leafless tree $T$, various algebraic groups over local fields might appear as closed subgroups of $\operatorname{Aut}(T)$. We show that the set of closed cocompact subgroups of $\operatorname{Aut}(T)$ that are isomorphic to a quasi-split simple algebraic group is a closed subset of the Chabauty space of $\operatorname{Aut}(T)$. This is done via a study of the integral Bruhat–Tits model of $\operatorname{SL}_{2}$ and $\operatorname{SU}_{3}^{L/K}$, that we carry on over arbitrary local fields, without any restriction on the (residue) characteristic. In particular, we show that in residue characteristic $2$, the Tits index of simple algebraic subgroups of $\operatorname{Aut}(T)$ is not always preserved under Chabauty limits.

scholarly journals Waring’s problem for unipotent algebraic groups

2019 ◽  
Vol 69 (4) ◽  
pp. 1857-1877 ◽  
Author(s):  
Michael Larsen ◽  
Dong Quan Ngoc Nguyen
Keyword(s):  
Algebraic Groups ◽  
Waring’S Problem ◽  
Waring's Problem ◽  
Unipotent Algebraic Groups

RESIDUAL PROPERTIES OF FREE PRO-P GROUPS

2001 ◽  
Vol 33 (5) ◽  
pp. 578-582 ◽  
Author(s):  
YIFTACH BARNEA
Keyword(s):  
Positive Characteristic ◽  
Congruence Subgroup ◽  
Probabilistic Method ◽  
Algebraic Groups ◽  
Local Fields ◽  
Random Generation ◽  
Zero Characteristic ◽  
Residual Properties ◽  
Characteristic Case ◽  
Lie Methods

Recall that if S is a class of groups, then a group G is residually-S if, for any element 1 ≠ g ∈ G, there is a normal subgroup N of G such that g ∉ N and G/N ∈ S. Let Λ be a commutative Noetherian local pro-p ring, with a maximal ideal M. Recall that the first congruence subgroup of SLd(Λ) is: SL1d(Λ) = ker (SLd(Λ) → SLd(Λ/M)).Let K ⊆ ℕ. We define SΛ(K) = ∪d∈K{open subgroups of SL1d(Λ)}. We show that if K is infinite, then for Λ = [ ]p[[t]] and for Λ = ℤp a finitely generated non-abelian free pro-p group is residually-SΛ(K). We apply a probabilistic method, combined with Lie methods and a result on random generation in simple algebraic groups over local fields. It is surprising that the case of zero characteristic is deduced from the positive characteristic case.

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