Sur l'homologie des groupes unitaires à coefficients polynomiaux

Publisher： Cambridge University Press

E-ISSN： 1865-5394|10|1|87-139

ISSN： 1865-2433

Source： Journal of K-Theory, Vol.10, Iss.1, 2012-08, pp. : 87-139

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Abstract

Let A be a ring with anti-involution and F a nice functor (tensor or symmetric power, for example) from finitely-generated projective A-modules to abelian groups. We show that the homology of the hyperbolic unitary groups U n,n(A) with coefficients in F(A2n ) can be expressed stably (i.e. after taking the colimit over n) by the homology of these groups with untwisted coefficients and functor homology groups that we can compute in suitable cases (for example, when A is a field of characteristic 0 or a ring without ℤ-torsion and F a tensor power). This extends the result where A is a finite field, which was dealt with previously by C. Vespa and the author (Ann. Sci. ENS, 2010).

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