La $R$-équivalence sur les tores

Colliot-Thélène, Jean-Louis; Sansuc, Jean-Jacques

doi:10.24033/asens.1325

Cited by 220 publications

(243 citation statements)

References 9 publications

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“…Background and references for the first part of the appendix (algebraic tori, quasi-trivial and flasque tori, groups of multiplicative type, R-equivalence) will be found in [2], [3], and [21]. For G a commutative algebraic group over a field k, theétale cohomogy group H 1 et (k, G) may be identified with a Galois cohomology group, and will be simply denoted H 1 (k, G).…”

Section: Corollariesmentioning

confidence: 99%

Rational Connectedness and Galois Covers of the Projective Line

Colliot-Thélène¹

2000

The Annals of Mathematics

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Section: Corollariesmentioning

confidence: 99%

Rational Connectedness and Galois Covers of the Projective Line

Colliot-Thélène¹

2000

The Annals of Mathematics

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“…The unramified Brauer group of the field k(X) with respect to k is a subgroup Brnr (k(X)lk) C Br (k(X)); it is isomorphic to the Brauer group of any smooth and proper model of X ( [G] This generalizes the construction due to Voskresenskii and Colliot-TheleneSansuc (see [V], [CS77]) when the X is the spectrum of a field. The natural map g* : (Br X )r -~ (Br Z)r is an isomorphism.…”

Section: Notation and Conventionsmentioning

confidence: 99%

The Brauer group of torsors and its arithmetic applications

Harari

Skorobogatov

2003

Annales De L’institut Fourier

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“…Also since C 3 is of order 2, ZN/HC 3 ⊗ G * n is stably permutation by [CT,Proposition 3,section 1]. Now adding W * p to both sides of…”

Section: Generic Matrices 3583mentioning

confidence: 99%

Induction theorems on the stable rationality of the center of the ring of generic matrices

Beneish

1998

Trans. Amer. Math. Soc.

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Abstract. Following Procesi and Formanek, the center of the division ring of n × n generic matrices over the complex numbers C is stably equivalent to the fixed field under the action of Sn, of the function field of the group algebra of a ZSn-lattice, denoted by Gn. We study the question of the stable rationality of the center Cn over the complex numbers when n is a prime, in this module theoretic setting. Let N be the normalizer of an n-sylow subgroup of Sn. Let M be a ZSn-lattice. We show that under certain conditions on M , inductionrestriction from N to Sn does not affect the stable type of the corresponding field. In particular, C(Gn) and C(ZG ⊗ ZN Gn) are stably isomorphic and the isomorphism preserves the Sn-action. We further reduce the problem to the study of the localization of Gn at the prime n; all other primes behave well. We also present new simple proofs for the stable rationality of Cn over C, in the cases n = 5 and n = 7.

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La $R$-équivalence sur les tores

Cited by 220 publications

References 9 publications

Rational Connectedness and Galois Covers of the Projective Line

Rational Connectedness and Galois Covers of the Projective Line

The Brauer group of torsors and its arithmetic applications

Induction theorems on the stable rationality of the center of the ring of generic matrices

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