Geodesic
Comparison of the discrete and continuous cohomology groups of a~pro-$p$ group
Algebra i analiz, Tome 19 (2007) no. 6, pp. 126-142.

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It is studied whether or not the natural map from the continuous to the discrete second cohomology group of a finitely generated pro-$p$ group is an isomorphism.
Keywords: Profinite group, comparison map. 
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G. A. Fernández-Alcober; I. V. Kazatchkov; V. N. Remeslennikov; P. Symonds. Comparison of the discrete and continuous cohomology groups of a~pro-$p$ group. Algebra i analiz, Tome 19 (2007) no. 6, pp. 126-142. http://geodesic.mathdoc.fr/item/AA_2007_19_6_a5/

[1] Barwise J. (ed.), Handbook of mathematical logic, Stud. Logic Found. Math., 90, North-Holland, Amsterdam etc., 1977 | MR

[2] Bousfield A. K., “On the $p$-adic completions of nonnilpotent spaces”, Trans. Amer. Math. Soc., 331 (1992), 335–359 | DOI | MR | Zbl

[3] Brown K. S., Cohomology of groups, Grad. Texts in Math., 87, Springer-Verlag, New York–Berlin, 1982 | MR

[4] Cartan H. et al., Algèbres d'Eilenberg-MacLane et homotopie, Séminaire Henri Cartan 7e année: 1954–1955, École Normale Supérieure, Paris, 1956

[5] Dixon J. D., du Sautoy M. P. F., Mann A., Segal D., Analytic pro-$p$ groups, 2nd ed., Cambridge Stud. in Adv. Math., 61, Cambridge Univ. Press, Cambridge, 1999 | MR | Zbl

[6] Friedlander E. M., Mislin G., “Cohomology of classifying spaces of complex Lie groups and related discrete groups”, Comment. Math. Helv., 59 (1984), 347–361 | DOI | MR | Zbl

[7] MacLane S., Homology, Grundlehren Math. Wiss., 114, Springer-Verlag, Berlin–New York, 1967 | MR

[8] Milnor J., “On the homology of Lie groups made discrete”, Comment. Math. Helv., 58 (1983), 72–85 | DOI | MR | Zbl

[9] Mislin G., private communication, 1997

[10] Ribes L., Zalesskii P., Profinite groups, Ergeb. Math. Grenzgeb. (3), 40, Springer-Verlag, Berlin, 2000 | MR | Zbl

[11] Serre J.-P., Cohomologie galoisienne, Lecture Notes in Math., 5, Springer-Verlag, Berlin, 1964

[12] Sury B., “Central extensions of $p$-adic groups; a theorem of Tate”, Comm. Algebra, 21 (1993), 1203–1213 | DOI | MR | Zbl

[13] Wilson J. S., Profinite groups, London Math. Soc. Monogr. New Ser., 19, Oxford Univ. Press, New York, 1998 | MR