On Grothendieck–Serre’s conjecture concerning principal -bundles over reductive group schemes: I
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Publication:5248727
DOI10.1112/S0010437X14007635zbMath1317.14102arXiv0905.1418OpenAlexW2551079978WikidataQ123191513 ScholiaQ123191513MaRDI QIDQ5248727
Anastasia Stavrova, Nikolai A. Vavilov, I. A. Panin
Publication date: 8 May 2015
Published in: Compositio Mathematica (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0905.1418
Group schemes (14L15) Linear algebraic groups over adèles and other rings and schemes (20G35) Linear algebraic groups and related topics (20G99) Exceptional groups (20G41)
Related Items (23)
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 ⋮ On the Grothendieck-Serre conjecture concerning principal \(G\)-bundles over semilocal Dedekind domains ⋮ A moving lemma for motivic spaces ⋮ Rigidity theorem for presheaves with $\Omega $-transfers ⋮ A proof of the Grothendieck-Serre conjecture on principal bundles over regular local rings containing infinite fields ⋮ Triangulated categories of framed bispectra and framed motives ⋮ Surjectivity of the étale excision map for homotopy invariant framed presheaves ⋮ A short proof of a theorem due to O. Gabber ⋮ Proof of the Grothendieck–Serre conjecture on principal bundles over regular local rings containing a field ⋮ Notes on a Grothendieck-Serre conjecture in mixed characteristic case ⋮ 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 classification of torsors over Laurent polynomial rings ⋮ Isotropic reductive groups over discrete Hodge algebras ⋮ Torsors of isotropic reductive groups over Laurent polynomials ⋮ Chevalley groups of type E7 in the 56-dimensional representation ⋮ A step towards the mixed-characteristic Grothendieck–Serre conjecture ⋮ Rationally isotropic quadratic spaces are locally isotropic. III ⋮ Nice triples and moving lemmas for motivic spaces ⋮ \(\mathbb{A}^1\)-invariance of non-stable \(K_1\)-functors in the equicharacteristic case ⋮ On the Grothendieck–Serre conjecture on principal bundles in mixed characteristic
Cites Work
- Homomorphismes abstraits de groupes algébriques simples
- Principal bundles on the affine line
- Principal homogeneous spaces under flasque tori; applications
- Indecomposable quadratic spaces over the affine plane
- Principal bundles on affine space and bundles on the projective line
- Locally trivial principal homogeneous spaces
- Reductive groups are geometrically reductive
- Affine homogeneous spaces and finite subgroups of arithmetic groups over function fields
- Principal bundles admitting a rational section
- Erratum: Principal bundles admitting a rational section
- Algebraic and abstract simple groups
- Invariants of a group in an affine ring
- Cancellation of Azumaya algebras
- General Néron desingularization and approximation
- Analytic isomorphism and category of finitely generated modules
- A purity theorem for the witt group
- \(\mathbb{A}^1\)-homotopy theory of schemes
- Rationally trivial Hermitian spaces are locally trivial
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