Rationality problems and conjectures of Milnor and Bloch–Kato

DOI10.1112/S0010437X13007021zbMath1279.14063arXiv1203.4022OpenAlexW3105654506WikidataQ122931440 ScholiaQ122931440MaRDI QIDQ2852241

Aravind Asok

Publication date: 8 October 2013

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1203.4022

zbMATH Keywords

Milnor conjectureunramified cohomologyrationalityunirationality\(\mathbb A^1\)-connectedness

Mathematics Subject Classification ID

Galois cohomology (12G05) Rational and unirational varieties (14M20) Algebraic theory of quadratic forms; Witt groups and rings (11E81) Motivic cohomology; motivic homotopy theory (14F42) Higher symbols, Milnor (K)-theory (19D45)

Related Items (7)

Torsion orders of Fano hypersurfaces ⋮ Birational classification of fields of invariants for groups of order 128 ⋮ Geometric criteria for 𝔸¹-connectedness and applications to norm varieties ⋮ Noether's problem for groups of order 243 ⋮ On the rationality problem for quadric bundles ⋮ Stably irrational hypersurfaces of small slopes ⋮ Degree three unramified cohomology groups and Noether's problem for groups of order 243

Cites Work

• Smooth varieties up to \(\mathbb A^1\)-homotopy and algebraic \(h\)-cobordisms
• On motivic cohomology with \(\mathbb{Z}/l\)-coefficients
• Noether's problem over an algebraically closed field
• An exact sequence for \(K^M_*/2\) with applications to quadratic forms
• Motivic cohomology of the simplicial motive of a Rost variety
• The Brauer group and the center of generic matrices
• Cohomologische Invarianten quadratischer Formen
• Variétés unirationelles non rationelles: Au-delà de l'exemple d'Artin et Mumford. (Non rational unirational varieties: Beyond the Artin-Mumford example)
• Unramified cohomology and rationality problems
• Motivic cohomology and unramified cohomology of quadrics
• Degree four cohomological invariants for quadratic forms
• Motivic cohomology with \(\mathbb Z/2\)-coefficients
• Unramified cohomology and the entire Hodge conjecture
• Norm varieties
• The stable \(\mathbb{A}^1\)-connectivity theorems
• Algebraic \(K\)-theory and quadratic forms. With an appendix by J. Tate
• Norm Varieties and the Chain Lemma (After Markus Rost)
• Families of rationally connected varieties
• Some Elementary Examples of Unirational Varieties Which are Not Rational
• Fields of \(u\)-invariant \(9\)

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