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The stable homology of congruence subgroups

Frank Calegari

Geometry & Topology 19 (2015) 3149–3191
Bibliography
1 A Ash, Galois representations attached to mod $p$ cohomology of $\mathrm{GL}(n,\mathbf{Z})$, Duke Math. J. 65 (1992) 235 MR1150586
2 H Bass, J Milnor, J P Serre, Solution of the congruence subgroup problem for $\mathrm{SL}_{n} (n\geq 3)$ and $\mathrm{Sp}_{2n} (n\geq 2)$, Inst. Hautes Études Sci. Publ. Math. (1967) 59 MR0244257
3 A Besser, P Buckingham, R de Jeu, X F Roblot, On the $p$–adic Beilinson conjecture for number fields, Pure Appl. Math. Q. 5 (2009) 375 MR2520465
4 A Borel, Stable real cohomology of arithmetic groups, Ann. Sci. École Norm. Sup. 7 (1974) 235 MR0387496
5 N Boston, J S Ellenberg, Pro-$p$ groups and towers of rational homology spheres, Geom. Topol. 10 (2006) 331 MR2224459
6 W Browder, J Pakianathan, Cohomology of uniformly powerful $p$–groups, Trans. Amer. Math. Soc. 352 (2000) 2659 MR1661313
7 F Calegari, Irrationality of certain $p$–adic periods for small $p$, Int. Math. Res. Not. 2005 (2005) 1235 MR2144087
8 F Calegari, N M Dunfield, Automorphic forms and rational homology $3$–spheres, Geom. Topol. 10 (2006) 295 MR2224458
9 F Calegari, M Emerton, Hecke operators on stable cohomology, arXiv:1311.5183
10 F Calegari, M Emerton, Mod–$p$ cohomology growth in $p$–adic analytic towers of 3-manifolds, Groups Geom. Dyn. 5 (2011) 355 MR2782177
11 F Calegari, M Emerton, Completed cohomology — a survey, from: "Non-abelian fundamental groups and Iwasawa theory" (editors J Coates, M Kim, F Pop, M Saidi, P Schneider), London Math. Soc. Lecture Note Ser. 393, Cambridge Univ. Press (2012) 239 MR2905536
12 F Calegari, D Geraghty, Modularity lifting beyond the Taylor–Wiles method, arXiv:1207.4224
13 F Calegari, A Venkatesh, A torsion Jacquet–Langlands correspondence, arXiv:1212.3847
14 R M Charney, Homology stability for $\mathrm{GL}_{n}$ of a Dedekind domain, Invent. Math. 56 (1980) 1 MR557579
15 R Charney, On the problem of homology stability for congruence subgroups, Comm. Algebra 12 (1984) 2081 MR747219
16 T Church, J S Ellenberg, B Farb, FI–modules and stability for representations of symmetric groups, Duke Math. J. 164 (2015) 1833
17 T Church, J S Ellenberg, B Farb, R Nagpal, FI–modules over Noetherian rings, Geom. Topol. 18 (2014) 2951 MR3285226
18 T Church, B Farb, Representation theory and homological stability, Adv. Math. 245 (2013) 250 MR3084430
19 H Cohen, H W Lenstra Jr., Heuristics on class groups of number fields, from: "Number theory, Noordwijkerhout 1983" (editor H Jager), Lecture Notes in Math. 1068, Springer (1984) 33 MR756082
20 H Darmon, F Diamond, R Taylor, Fermat's last theorem, from: "Elliptic curves, modular forms & Fermat's last theorem" (editors J Coates, S T Yau), Int. Press (1997) 2 MR1605752
21 P Deligne, Extensions centrales non résiduellement finies de groupes arithmétiques, C. R. Acad. Sci. Paris Sér. A-B 287 (1978) MR507760
22 L Evens, E M Friedlander, On $K_\ast(\mathbf{Z}/p^{2}\mathbf{Z})$ and related homology groups, Trans. Amer. Math. Soc. 270 (1982) 1 MR642328
23 O Gabber, $K$–theory of Henselian local rings and Henselian pairs, from: "Algebraic $K$–theory, commutative algebra, and algebraic geometry" (editors R K Dennis, C Pedrini, M R Stein), Contemp. Math. 126, Amer. Math. Soc. (1992) 59 MR1156502
24 R Greenberg, Iwasawa theory for $p$–adic representations, from: "Algebraic number theory" (editors J Coates, R Greenberg, B Mazur, I Satake), Adv. Stud. Pure Math. 17, Academic Press (1989) 97 MR1097613
25 L Hesselholt, I Madsen, On the $K$–theory of local fields, Ann. of Math. 158 (2003) 1 MR1998478
26 M Lazard, Groupes analytiques $p$–adiques, Inst. Hautes Études Sci. Publ. Math. (1965) 389 MR0209286
27 R Lee, R H Szczarba, The group $K_{3}(Z)$ is cyclic of order forty-eight, Ann. of Math. 104 (1976) 31 MR0442934
28 J McCleary, A user's guide to spectral sequences, Cambridge Studies in Advanced Mathematics 58, Cambridge Univ. Press (2001) MR1793722
29 J S Milne, Arithmetic duality theorems, BookSurge (2006) MR2261462
30 J W Milnor, J C Moore, On the structure of Hopf algebras, Ann. of Math. 81 (1965) 211 MR0174052
31 J A Neisendorfer, Homotopy groups with coefficients, J. Fixed Point Theory Appl. 8 (2010) 247 MR2739026
32 I A Panin, The Hurewicz theorem and $K$–theory of complete discrete valuation rings, Izv. Akad. Nauk SSSR Ser. Mat. 50 (1986) 763, 878 MR864175
33 A Putman, Stability in the homology of congruence subgroups, arXiv:1201.4876
34 D Quillen, On the cohomology and $K$–theory of the general linear groups over a finite field, Ann. of Math. 96 (1972) 552 MR0315016
35 D Quillen, Finite generation of the groups $K_{i}$ of rings of algebraic integers, from: "Algebraic $K$–theory, I: Higher $K$–theories", Lecture Notes in Math. 341, Springer (1973) 179 MR0349812
36 P Schneider, Über gewisse Galoiscohomologiegruppen, Math. Z. 168 (1979) 181 MR544704
37 P Schneider, Über die Werte der Riemannschen Zetafunktion an den ganzzahligen Stellen, J. Reine Angew. Math. 313 (1980) 189 MR552472
38 P Scholze, On torsion in the cohomology of locally symmetric varieties, arXiv:1306.2070
39 C Soulé, $K$–théorie des anneaux d'entiers de corps de nombres et cohomologie étale, Invent. Math. 55 (1979) 251 MR553999
40 C Soulé, On higher $p$–adic regulators, from: "Algebraic $K$–theory" (editors E M Friedlander, M R Stein), Lecture Notes in Math. 854, Springer (1981) 372 MR618313
41 J Tate, Duality theorems in Galois cohomology over number fields, from: "Proc. Internat. Congr. Mat. (Stockholm, 1962)", Inst. Mittag-Leffler (1963) 288 MR0175892
42 V Voevodsky, On motivic cohomology with $\mathbf{Z}/l$–coefficients, Ann. of Math. 174 (2011) 401 MR2811603
43 J B Wagoner, Continuous cohomology and $p$–adic $K$–theory, from: "Algebraic $K$–theory" (editor M R Stein), Lecture Notes in Math. 551, Springer (1976) 241 MR0498502
44 J B Wagoner, A $p$–adic regulator problem in algebraic $K$–theory and group cohomology, Bull. Amer. Math. Soc. 10 (1984) 101 MR722861
45 C Weibel, Algebraic $K$–theory of rings of integers in local and global fields, from: "Handbook of $K$–theory, Vol. 1, 2" (editors E M Friedlander, D R Grayson), Springer (2005) 139 MR2181823
46 C A Weibel, The $K$–book: An introduction to algebraic $K$–theory, Graduate Studies in Mathematics 145, Amer. Math. Soc. (2013) MR3076731
47 A Wiles, The Iwasawa conjecture for totally real fields, Ann. of Math. 131 (1990) 493 MR1053488
48 A Wiles, Modular elliptic curves and Fermat's last theorem, Ann. of Math. 141 (1995) 443 MR1333035
49 E C Zeeman, A note on a theorem of Armand Borel, Proc. Cambridge Philos. Soc. 54 (1958) 396 MR0105099