Homotopy invariance of non-stable K1-functors

DOI10.1017/is013006012jkt232zbMath1314.19002arXiv1111.4664OpenAlexW2964194134MaRDI QIDQ3191174

Anastasia Stavrova

Publication date: 24 September 2014

Published in: Journal of K-Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.4664

zbMATH Keywords

Whitehead groupelementary subgroupChevalley commutator formulaisotropic reductive groupnon-stable \(K_{1}\)-unctor

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Classical groups (algebro-geometric aspects) (14L35) (K_1) of group rings and orders (19B28) Structure theory for linear algebraic groups (20G07)

Related Items (23)

On the complete intersection conjecture of Murthy ⋮ Bounded reduction of orthogonal matrices over polynomial rings ⋮ On the number of generators of ideals in polynomial rings ⋮ A local-global principle for symplectic \(\mathrm K_2\) ⋮ On the Grothendieck-Serre conjecture concerning principal \(G\)-bundles over semilocal Dedekind domains ⋮ The commutators of classical groups ⋮ Erratum to: ``On the complete intersection conjecture of Murthy ⋮ Bounded reduction for Chevalley groups of types \(E_6\) and \(E_7\) ⋮ On \(\mathbb{A}^1\)-fundamental groups of isotropic reductive groups ⋮ Monic inversion principle and complete intersection ⋮ On the congruence kernel of isotropic groups over rings ⋮ Relating the Principles of Quillen–Suslin Theory ⋮ Affine representability results in \(\mathbb A^1\)-homotopy theory. II: Principal bundles and homogeneous spaces ⋮ Local-global principle for congruence subgroups of Chevalley groups. ⋮ Isotropic reductive groups over discrete Hodge algebras ⋮ Chevalley groups of polynomial rings over Dedekind domains ⋮ ``\({\mathbb{P}}^1\)-gluing for local complete intersections ⋮ Calculations in exceptional groups, an update. ⋮ \(\mathbb{A}^1\)-invariance of non-stable \(K_1\)-functors in the equicharacteristic case ⋮ A Horrocks-type theorem for even orthogonal \(K_2\) ⋮ On abstract homomorphisms of some special unitary groups ⋮ Multiple commutator formulas for unitary groups ⋮ Homotopy and commutativity principle

Cites Work

• The Tits indices over semilocal rings.
• Localization-completion strikes again: relative \(K_1\) is nilpotent by Abelian
• On the homotopy groups of algebraic groups
• Principal homogeneous spaces under flasque tori; applications
• A module structure on certain orbit sets of unimodular rows
• On the Bass-Quillen conjecture concerning projective modules over polynomial rings
• Quadratic modules and the orthogonal group over polynomial rings
• Locally trivial principal homogeneous spaces
• On the groups \(\mathrm{SL}_ 2(\mathbb{Z}[x)\) and \(\mathrm{SL}_ 2(k[x,y])\)]
• The structure of the group \(G(k[t)\): variations on a theme of Soulé.]
• On symplectic groups over polynomial rings
• Algebraic and abstract simple groups
• Groupes reductifs
• Complements à l'article: Groupes reductifs
• Elementary subgroup of an isotropic reductive group is perfect
• Elementary subgroups of isotropic reductive groups
• Local-global principle for transvection groups
• ¹-Homotopy of Chevalley Groups
• Whitehead groups of chevalley groups over polynomial rings
• The general linear group of polynomial rings over regular rings
• ON THE STRUCTURE OF THE SPECIAL LINEAR GROUP OVER POLYNOMIAL RINGS
• Free quotients of 𝑆𝐿₂(𝑅[𝑥)]
• Letter to the editor: General Néron desingularization and approximation
• Projective modules over polynomial rings

This page was built for publication: Homotopy invariance of non-stable K₁-functors