Symbol algebras and cyclicity of algebras after a scalar extension

Rehmann, Ulf; Tikhonov, Sergey V.; Yanchevskii, V. I.

doi:10.1007/s10958-009-9742-2

Cited by 6 publications

(7 citation statements)

References 15 publications

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“…Replacing F by a field extension over which A has index exactly p 2 and replacing A by a Brauer equivalent division algebra, we may assume that A is a division algebra of degree p 2 . Moreover, an application of the index reduction formula shows that we may assume that A is decomposable, i.e., A is a tensor product of two algebras of degree p (see [19,Theorem 1.20]). …”

Section: Not Surjective Then Suslin's Conjecture Holds For Amentioning

confidence: 99%

Suslin’s conjecture on the reduced Whitehead group of a simple algebra

Merkurjev

2015

J. Amer. Math. Soc.

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Section: Not Surjective Then Suslin's Conjecture Holds For Amentioning

confidence: 99%

Suslin’s conjecture on the reduced Whitehead group of a simple algebra

Merkurjev

2015

J. Amer. Math. Soc.

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“…Récemment Rehman-Tikhonov-Yanchevskiȋ ont en plus démontré qu'il suffit de vérifier la conjecture de Suslin pour des algèbresà division cycliques. Il suffit même de démontrer la conjecture pour une classe d'algèbresà division cycliquesélémentaires (des produits tensoriels de deux algèbres cycliques de Dickson) [RTY,.…”

Section: Conjecture De Suslinunclassified

“…Suslin a conjecturé la réciproque [Sus1]. Récemment, Merkurjev a démontré que cette conjecture vaut si 4 | ind k (A) [Mer2], et Rehman-Tikhonov-Yanchevskiȋ ont démontré qu'il suffit de démontrer la conjecture pour des algèbresà division cycliques [RTY,Thm. 0.19].…”

Section: Introductionunclassified

L'invariant de Suslin en caractéristique positive

Wouters¹

2010

J. K-Theory

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RÉSUMÉPour une k-algèbre simple centrale A d'indice inversible dans k, Suslin a défini un invariant cohomologique de SK1 (A) ‘Sus2’. Dans ce texte, nous généralisons cet invariant à toute k-algèbre simple centrale par un relèvement de la caractéristique positive à la caractéristique 0. Pour pouvoir définir cet invariant, on a besoin des groupes de cohomologie des différentielles logarithmiques de Kato [Kat1].

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“…This would give a sufficient answer to the question of Tannaka and Artin. Merkurjev proved it is true when 4 | ind k (A) [Mer3]; and Rehmann-Tikhonov-Yanchevskiȋ proved it is sufficient to prove the conjecture for the tensor product of two symbol algebras [RTY,Thm. 0.19].…”

Section: Introductionmentioning

confidence: 99%

Comparing Invariants of SK1

Wouters

2011

Algebr Represent Theor

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In this text, we compare several invariants of the reduced Whitehead group SK 1 of a central simple algebra.For biquaternion algebras, we compare a generalised invariant of Suslin as constructed by the author in [Wou] to an invariant introduced by Knus-Merkurjev-Rost-Tignol [KMRT]. Using explicit computations, we prove these invariants are essentially the same.We also prove the non-triviality of an invariant introduced by Kahn [Kah2]. To obtain this result, we compare Kahn's invariant to an invariant introduced by Suslin in 1991 [Sus1] which is non-trivial for Platonov's examples of non-trivial SK 1 [Pla]. We also give a formula for the value on the centre of the tensor product of two symbol algebras which generalises a formula of Merkurjev for biquaternion algebras [Mer1].

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Symbol algebras and cyclicity of algebras after a scalar extension

Cited by 6 publications

References 15 publications

Suslin’s conjecture on the reduced Whitehead group of a simple algebra

Suslin’s conjecture on the reduced Whitehead group of a simple algebra

L'invariant de Suslin en caractéristique positive

Comparing Invariants of SK1

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