The congruence kernel of an arithmetic lattice in a rank one algebraic group over a local field

DOI10.1515/CRELLE.2008.072zbMath1162.20031arXiv0710.4009OpenAlexW2099574837MaRDI QIDQ3542072

Alexander Premet, Balasubramanian Sury, Pavel A. Zalesskii, Alexander W. Mason

Publication date: 27 November 2008

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0710.4009

zbMATH Keywords

free profinite productscongruence subgroup problemsimply-connected algebraic groupsarithmetic latticescongruence kernels

Mathematics Subject Classification ID

Unimodular groups, congruence subgroups (group-theoretic aspects) (20H05) Discrete subgroups of Lie groups (22E40) Structure of modular groups and generalizations; arithmetic groups (11F06) Linear algebraic groups over local fields and their integers (20G25)

Related Items (3)

Genuine non-congruence subgroups of Drinfeld modular groups ⋮ On the congruence kernel for simple algebraic groups ⋮ Groups with infinite mod-\(p\) Schur multiplier.

Cites Work

• Congruence hulls in \(SL_ n\)
• Free quotients and the congruence kernel of \(SL_ 2\).
• Lattices in rank one Lie groups over local fields
• A non-abelian free pro-\(p\) group is not linear over a local field
• Cusps of lattices in rank 1 Lie groups over local fields
• Profinite surface groups and the congruence kernel of arithmetic lattices in \(\text{SL}_2(\mathbb{R})\).
• On periodic compact groups
• Nilpotent orbits in good characteristic and the Kempf-Rousseau theory
• Nilpotent orbits over ground fields of good characteristic
• Quotients of the congruence kernels of \(\text{SL}_ 2\) over arithmetic Dedekind domains
• Le problème des groupes de congruence pour \(SL_2\)
• Eigenvalues of the Laplacian, the first Betti number and the congruence subgroup problem
• Tame Subgroup of a Semi-Simple Group Over a Local Field

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