2006
DOI: 10.1016/j.jalgebra.2006.01.038
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Reduced K-theory of Azumaya algebras

Abstract: In the theory of central simple algebras, often we are dealing with abelian groups which arise from the kernel or co-kernel of functors which respect transfer maps (for example K-functors). Since a central simple algebra splits and the functors above are "trivial" in the split case, one can prove certain calculus on these functors. The common examples are kernel or co-kernel of the maps K i (F ) → K i (D), where K i are Quillen K-groups, D is a division algebra and F its center, or the homotopy fiber arising f… Show more

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Cited by 5 publications
(5 citation statements)
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“…The aim of this note is to prove that for the Hensel pair (R, I) where R is a semilocal ring, the map SK 1 (A) → SK 1 (A) is also an isomorphism. This extends a result of [6] to non-local Henselian rings.…”
supporting
confidence: 82%
“…The aim of this note is to prove that for the Hensel pair (R, I) where R is a semilocal ring, the map SK 1 (A) → SK 1 (A) is also an isomorphism. This extends a result of [6] to non-local Henselian rings.…”
supporting
confidence: 82%
“…They used the Skolem-Noether theorem. That case has also been proven by Hazrat [7] using the fact that A isétale locally a matrix algebra.…”
Section: The Kernel Of Bmentioning
confidence: 55%
“…Now consider the group CK 1 (A) = A * /R * A for the Azumaya algebra A over the Hensel pair (R, I ). A proof similar to Theorem 3.10 in [6], shows that CK 1 (A) ∼ = CK 1 (A). Thus in the case of tame unramified division algebra D, one can observe that CK 1 (D) ∼ = CK 1 (D).…”
Section: Corollary 2 Let a Be An Azumaya Algebra Over A Hensel Pair (mentioning
confidence: 65%