Homotopy invariance of non-stable K1-functors
2013 ◽
Vol 13
(2)
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pp. 199-248
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Keyword(s):
AbstractLet G be a reductive algebraic group over a field k, such that every semisimple normal subgroup of G has isotropic rank ≥ 2, i.e. contains (Gm)2. Let K1G be the non-stable K1-functor associated to G, also called the Whitehead group of G. We show that K1G(k) = K1G (k[X1 ,…, Xn]) for any n ≥ 1. If k is perfect, this implies that K1G (R) = K1G (R[X]) for any regular k-algebra R. If k is infinite perfect, one also deduces that K1G (R) → K1G (K) is injective for any local regular k-algebra R with the fraction field K.
1971 ◽
Vol 12
(1)
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pp. 1-14
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2019 ◽
Vol 2019
(754)
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pp. 1-15
1982 ◽
Vol 92
(1)
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pp. 65-72
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2014 ◽
Vol 14
(3)
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pp. 493-575
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1983 ◽
Vol 27
(3)
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pp. 361-379
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Keyword(s):