1996
DOI: 10.1007/bf02698837
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R-equivalence and rationality problem for semisimple adjoint classical algebraic groups

Abstract: L'accès aux archives de la revue « Publications mathématiques de l'I.H.É.S. » (http:// www.ihes.fr/IHES/Publications/Publications.html) implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques ht… Show more

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Cited by 37 publications
(29 citation statements)
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“…The main ingredients in proofs of our results are Merkurjev's computation of G(F )/R for all adjoint groups of classical type [Me2,Th. 1], as well as results on the classification of hermitian forms over division algebras with involution over fields of virtual cohomological dimension two [BP2].…”
Section: Introductionmentioning
confidence: 98%
“…The main ingredients in proofs of our results are Merkurjev's computation of G(F )/R for all adjoint groups of classical type [Me2,Th. 1], as well as results on the classification of hermitian forms over division algebras with involution over fields of virtual cohomological dimension two [BP2].…”
Section: Introductionmentioning
confidence: 98%
“…The algebraic group G is called R-trivial if G(L)/R = 1 for every field extension L/F . It was established by ColliotThélène and Sansuc in [2] (see also [7,Proposition 1]) that the group G is R-trivial if the variety of G is stably rational.…”
Section: Introductionmentioning
confidence: 99%
“…of Th. 8] proved that adjoint groups of type 2 A n are rational if n is even, and Merkurjev [7,Prop. 4] showed that adjoint groups of type C n are stably rational for n odd.…”
Section: Introductionmentioning
confidence: 99%
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