Stability of unitary SK1 of Azumaya algebras

Hazrat, Roozbeh

doi:10.1007/s00013-011-0338-y

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2014

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“…As a corollary, we obtain the following result. The corresponding statement was previously known for general isotropic simply connected groups G over Henselian discrete valuation rings [G1], [G2,Corollaire 7.3], and for groups G of type A l over arbitrary Henselian local rings [Haz10,Haz12].…”

Section: Introductionmentioning

confidence: 85%

Transfers for non-stable K_1-functors of classical type

Stavrova

2014

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Let k be a field. Let G be an absolutely almost simple simply connected kgroup of type A l , l ≥ 2, or D l , l ≥ 4, containing a 2-dimensional split torus. If G is of type D l , assume moreover that char k = 2. We show that the Nisnevich sheafification of the non-stable K 1 -functor K G 1 , also called the Whitehead group of G, on the category of smooth k-schemes is A 1 -invariant, and has oriented weak transfers for affine varieties in the sense of Panin-Yagunov-Ross. If k has characteristic 0, this implies that the Nisnevich sheafification of K G 1 is birationally invariant. We also prove a rigidity theorem for A 1 -invariant torsion presheaves with oriented weak transfers over infinite fields. As a corollary, we conclude that K G 1 (R) = K G 1 (k) whenever R is a Henselian regular local ring with a coefficient field k.

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Section: Introductionmentioning

confidence: 85%

Transfers for non-stable K_1-functors of classical type

Stavrova

2014

Preprint

View full text Add to dashboard Cite

show abstract

Stability of unitary SK1 of Azumaya algebras

Cited by 1 publication

References 13 publications

Transfers for non-stable K_1-functors of classical type

Transfers for non-stable K_1-functors of classical type

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