Proof of the Grothendieck–Serre conjecture on principal bundles over regular local rings containing a field

DOI10.1070/IM8982zbMath1458.14024OpenAlexW2981711282WikidataQ123342577 ScholiaQ123342577MaRDI QIDQ5118070

I. A. Panin

Publication date: 4 September 2020

Published in: Izvestiya: Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/im8982

zbMATH Keywords

reductive group schemesprincipal bundlesGrothendieck-Serre conjecture

Mathematics Subject Classification ID

Étale and other Grothendieck topologies and (co)homologies (14F20) Cohomology theory for linear algebraic groups (20G10) Linear algebraic groups over local fields and their integers (20G25) Group schemes (14L15) Linear algebraic groups over adèles and other rings and schemes (20G35) Group varieties (14L10)

Related Items (13)

Problems about torsors over regular rings ⋮ On the Grothendieck-Serre conjecture about principal bundles and its generalizations ⋮ Grothendieck–Serre in the quasi-split unramified case ⋮ Special groups, versality and the Grothendieck-Serre conjecture ⋮ Strong A1${\mathbb {A}}^1$‐invariance of A1${\mathbb {A}}^1$‐connected components of reductive algebraic groups ⋮ An 8-periodic exact sequence of Witt groups of Azumaya algebras with involution ⋮ The Grothendieck–Serre conjecture over valuation rings ⋮ A short exact sequence ⋮ Nice triples and the Grothendieck-Serre conjecture concerning principal G-bundles over reductive group schemes ⋮ Two purity theorems and the Grothendieck-Serre conjecture concerning principal -bundles ⋮ A step towards the mixed-characteristic Grothendieck–Serre conjecture ⋮ \(\mathbb{A}^1\)-invariance of non-stable \(K_1\)-functors in the equicharacteristic case ⋮ On the Grothendieck–Serre conjecture on principal bundles in mixed characteristic

Cites Work

• Nice triples and the Grothendieck-Serre conjecture concerning principal G-bundles over reductive group schemes
• A proof of the Grothendieck-Serre conjecture on principal bundles over regular local rings containing infinite fields
• Locally trivial principal homogeneous spaces
• Torsors on the affine line
• Schémas en groupes. I: Propriétés générales des schémas en groupes. Exposés I à VIIb. Séminaire de Géométrie Algébrique 1962/64, dirigé par Michel Demazure et Alexander Grothendieck. Revised reprint
• Bertini theorems over finite fields
• Bertini irreducibility theorems over finite fields
• A purity theorem for the witt group
• ON GROTHENDIECK–SERRE CONJECTURE CONCERNING PRINCIPAL BUNDLES
• Nice triples and moving lemmas for motivic spaces
• On Grothendieck–Serre’s conjecture concerning principal -bundles over reductive group schemes: I
• Rationally trivial Hermitian spaces are locally trivial
• Unnamed Item
• Unnamed Item

This page was built for publication: Proof of the Grothendieck–Serre conjecture on principal bundles over regular local rings containing a field