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Let $K$ be a non-archimedean local field. This paper gives an explicit isomorphism between the dual of the special representation of $G L_{n + 1} (K)$ and the space of harmonic cochains defined on the Bruhat-Tits building of $G L_{n + 1} (K)$ , in the sense of E. de Shalit [11]. We deduce, applying the results of a paper of P. Schneider and U. Stuhler [9], that there exists a $G L_{n + 1} (K)$ -equivariant isomorphism between the cohomology group of the Drinfeld symmetric space and the space of harmonic cochains.

Cohomology of finite groups of Lie type, I

Edward Cline, Brian Parshall, Leonard Scott (1975)

Publications Mathématiques de l'IHÉS

Cohomology of groups, Abelian Sylow subgroups and splendid equivalences.

Zimmermann, Alexander (2000)

AMA. Algebra Montpellier Announcements [electronic only]

Cohomology of groups with operators.

Cegarra, A.M., García-Calcines , J.M., Ortega, J.A. (2002)

Homology, Homotopy and Applications

Cohomology of Induced Representations for Algebraic Groups.

Henning Haahr Andersen, Jens Carsten Jantzen (1984)

Mathematische Annalen

Cohomology of infinitesimal algebraic groups.

M. Kaneda, N. Shimada, M. Tezuka (1990)

Mathematische Zeitschrift

Cohomology of Infinitesimal and Discrete Groups.

Eric M. Friedlander, Brian J. Parshall (1985/1986)

Mathematische Annalen

Cohomology of integer matrices and local-global divisibility on the torus

Marco Illengo (2008)

Journal de Théorie des Nombres de Bordeaux

Let $p \neq 2$ be a prime and let $G$ be a $p$ -group of matrices in ${SL}_{n} (ℤ)$ , for some integer $n$ . In this paper we show that, when $n < 3 (p - 1)$ , a certain subgroup of the cohomology group $H^{1} (G, 𝔽_{p}^{n})$ is trivial. We also show that this statement can be false when $n \geq 3 (p - 1)$ . Together with a result of Dvornicich and Zannier (see [2]), we obtain that any algebraic torus of dimension $n < 3 (p - 1)$ enjoys a local-global principle on divisibility by $p$ .

Cohomology of Lie groups made discrete.

Pere Pascual Gainza (1990)

Publicacions Matemàtiques

We give a survey of the work of Milnor, Friedlander, Mislin, Suslin and other authors on the Friedlander-Milnor conjecture on the homology of Lie groups made discrete and its relation to the algebraic K-theory of fields.

Cohomology of line bundles on $G / B$

Lakshmi Bai, C. Musili, C. S. Seshadri (1974)

Annales scientifiques de l'École Normale Supérieure

Cohomology of line bundles on $G / B$

Henning Haahr Andersen (1979)

Annales scientifiques de l'École Normale Supérieure

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