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Torsion classes in the cohomology of congruence subgroups

Published online by Cambridge University Press:  24 October 2008

Dominique Arlettaz
Dominique Arlettaz
Affiliation:
Département de Mathématiques, Ecole Polytechnique Fédérate, CH-1015 Lausanne, Switzerland
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Extract

For any prime number p, let Γn, p denote the congruence subgroup of SLn(ℤ) of level p, i.e. the kernel of the surjective homomorphism fp: SLn(ℤ) → SLn(p) induced by the reduction mod p (Fp is the field with p elements). We define

using upper left inclusions Γn, p ↪ Γn+1, p. Recall that the groups Γn, p are homology stable with M-coefficients, for instance if M = ℚ, ℤ[1/p], or ℤ/q with q prime and q ╪ p: Hi(Γn, p; M) ≅ Hi(Γp; M) for n ≥ 2i + 5 from [7] (but the homology stability fails if M = ℤ or ℤ/p).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 105 , Issue 2 , March 1989 , pp. 241 - 248
Copyright
Copyright © Cambridge Philosophical Society 1989

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References

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