Homology stability for unitary groups over S-arithmetic rings
2010 ◽
Vol 8
(2)
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pp. 293-322
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Keyword(s):
Ad Hoc
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AbstractWe prove that the homology of unitary groups over rings of S-integers in number fields stabilizes. Results of this kind are well known to follow from the high acyclicity of ad-hoc polyhedra. Given this, we exhibit two simple conditions on the arithmetic of hermitian forms over a ring A relatively to an anti-automorphism which, if they are satisfied, imply the stabilization of the homology of the corresponding unitary groups. When R is a ring of S-integers in a number field K, and A is a maximal R-order in an associative composition algebra F over K, we use the strong approximation theorem to show that both of these properties are satisfied. Finally we take a closer look at the case of On(ℤ[½]).
2005 ◽
Vol 21
(6)
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pp. 1269-1276
1999 ◽
Vol 100
(3)
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pp. 499-513
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Keyword(s):
1991 ◽
Vol 88
(3)
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pp. 381-404
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2002 ◽
Vol 42
(3)
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pp. 477-484
1976 ◽
Vol 63
◽
pp. 153-162
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