Noether's problem over an algebraically closed field

DOI10.1007/BF01389135zbMath0546.14014OpenAlexW2110254688MaRDI QIDQ798390

Publication date: 1984

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143138

zbMATH Keywords

Galois extensions algebraically closed field Brauer group rationality of function field retract rational field

Mathematics Subject Classification ID

Separable extensions, Galois theory (12F10) Actions of groups on commutative rings; invariant theory (13A50) Extension theory of commutative rings (13B02) Galois theory and commutative ring extensions (13B05)

Related Items

Unnamed Item, Rationality Problem for Algebraic Tori, Finite solvable groups with a rational skew-field of noncommutative real rational invariants, The Lüroth Problem, Noether’s Problem for Some p-Groups, Bogomolov multipliers for some \(p\)-groups of nilpotency class 2, Degree three unramified cohomology groups, Generic Picard-Vessiot extensions for connected-by-finite groups., On Noether's problem for central extensions of symmetric and alternating groups, Multiplicative field invariants, Algebras of general type: rational parametrization and normal forms, Groups of order \(p^5\) and their unramified Brauer groups, Noether's Problem for p-Groups with an Abelian Subgroup of Index p, Erratum to ``Localization on singular varieties, The rationality problem for conic bundles, Rationality of the moduli spaces of plane curves of sufficiently large degree, Torsion orders of Fano hypersurfaces, \(H^3\) and generic matrices, Noether's problem on semidirect product groups, Cohomologie des groupes et corps d'invariants multiplicatifs. (Cohomology of groups and fields of multiplicative invariants), On the Hasse principle for homogeneous spaces with finite stabilizers, Galois groups of orderP³, Noether's problem for \(p\)-groups with a cyclic subgroup of index \(p^{2}\), On the exponent of Bogomolov multipliers, Local-global invariants of finite and infinite groups: around Burnside from another side., On images of affine spaces, Noether Settings of Some Groups with an Unexpected Property, Rationality of homogeneous varieties, Birational classification of fields of invariants for groups of order 128, Faithful actions of automorphism groups of free groups on algebraic varieties, Bogomolov multipliers and retract rationality for semidirect products, An exact sequence and triviality of Bogomolov multiplier of groups, Versal torsors and retracts, The Ekedahl invariants for finite groups, On the mixed Tate property and the motivic class of the classifying stack of a finite group, On the dual of the Procesi-Formanek lattice., Bogomolov multiplier of Lie algebras, Non-rational varieties with the Hilbert Property, Retract rational fields, Cohomological invariants of algebraic stacks, Stable rationality of certain invariant fields., Frobenius groups and retract rationality, Unramified cohomology of quadrics in characteristic two, Twisted multiplicative field invariants, Noether's problem, and Galois extensions, Rationality of the quotient of \(\mathbb P^2\) by finite group of automorphisms over arbitrary field of characteristic zero, The Bogomolov multiplier of rigid finite groups, Unramified cohomology of alternating groups., Noether’s problem for orientation p-subgroups of symmetric groups, Zéro-cycles sur les espaces homogènes et problème de Galois inverse, Noether's problem for groups of order 243, Some aspects of noncommutative invariant theory and the Noether's problem, Unramified cohomology of degree 3 and Noether's problem, The image of the map from group cohomology to Galois cohomology, Some new parallels between groups and Lie algebras, or what can be simpler than multiplication table?, The Bogomolov multiplier of Lie algebras, Noether's problem for groups of order 32, Degree three invariants for semisimple groups of types \(B\), \(C\), and \(D\), Reduction in the rationality problem for multiplicative invariant fields, Rationality of \(P\)-group actions, Counting points of homogeneous varieties over finite fields, Motivic classes and the integral Hodge question, Noether's problem for metacyclic \(p\)-groups, Chow's theorem for semi-abelian varieties and bounds for splitting fields of algebraic tori, NOETHER SETTINGS FOR CENTRAL EXTENSIONS OF GROUPS WITH ZERO SCHUR MULTIPLIER, Degree 3 unramified cohomology of classifying spaces for exceptional groups, The quotient map on the equivariant Grothendieck ring of varieties, \(R\)-equivalence of \(G\)-coverings over non-Archimedean local fields, The Noether problem for spinor groups of small rank, Rationality problem for some meta-abelian groups, Lattices over cyclic groups and Noether settings, The tight approximation property, The Noether problem for Hopf algebras, Variétés unirationelles non rationelles: Au-delà de l'exemple d'Artin et Mumford. (Non rational unirational varieties: Beyond the Artin-Mumford example), Cohomology of certain moduli spaces of vector bundles, Bogomolov multiplier and the Lazard correspondence, Bogomolov multipliers of some groups of order p⁶, On Bogomolov multiplier and \(\Sha\)-rigidity of groups, On Schur's exponent property and its relation to Noether's Rationality problem, Birational geometry of linear algebraic groups and Galois modules, The noncommutative Noether's problem is almost equivalent to the classical Noether's problem, Rationality of some projective linear actions, Cycles, derived categories, and rationality, Noncommutative rational functions invariant under the action of a finite solvable group, Rationality for Subgroups ofS₆, Motivic classes of classifying stacks of some semi-direct products, Degree three unramified cohomology groups and Noether's problem for groups of order 243, Rationality problems and conjectures of Milnor and Bloch–Kato, Stable rationality of the field of invariants of linear representations of the group \(PSL_ 6\) and \(PSL_{12}\), Unramified cohomology and rationality problems, The ambiguity index of an equipped finite group., Free actions on surfaces that do not extend to arbitrary actions on 3-manifolds, On Noether's problem for cyclic groups of prime order, Multiplicative Invariant Fields of Dimension ≤6, Unramified degree three invariants of reductive groups

Cites Work