Geometry & Topology
- Geom. Topol.
- Volume 19, Number 6 (2015), 3149-3191.
The stable homology of congruence subgroups
We relate the completed cohomology groups of , where is the ring of integers of a number field, to –theory and Galois cohomology. Various consequences include showing that Borel’s stable classes become infinitely –divisible up the –congruence tower if and only if a certain –adic zeta value is nonzero. We use our results to compute (for sufficiently large ), where is the full level- congruence subgroup of .
Geom. Topol., Volume 19, Number 6 (2015), 3149-3191.
Received: 7 November 2013
Revised: 27 December 2014
Accepted: 26 January 2015
First available in Project Euclid: 16 November 2017
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Calegari, Frank. The stable homology of congruence subgroups. Geom. Topol. 19 (2015), no. 6, 3149--3191. doi:10.2140/gt.2015.19.3149. https://projecteuclid.org/euclid.gt/1510858872