Stable cohomology of congruence subgroups
Abstract
Abstract We describe the double struck upper F Subscript p F p $\mathbb{F}_p$ -cohomology of the congruence subgroups normal upper S normal upper L Subscript n Baseline left parenthesis double struck upper Z comma p Superscript m Baseline right parenthesis S L n ( Z , p m ) $\mathrm{SL}_n(\mathbb{Z}, p^m)$ in degrees asterisk less than p minus 1 ∗ < p − 1 $* \lt p-1$ , for all large enough n , establishing a formula proposed by F. Calegari. Along the way, we also establish a formula for the stable cohomology of normal upper S normal upper L Subscript n Baseline left parenthesis double struck upper Z divided by p right parenthesis S L n ( Z / p ) $\mathrm{SL}_n(\mathbb{Z}/p)$ with certain twisted coefficients.
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Advanced Algebra and Geometry
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Compositio Mathematica
- Publisher
- Cambridge University Press (CUP)
- Volume
- 162
- Issue
- 6
- Pages
- 1274–1317
- Publication date
- 1 June 2026
- Language
- EN