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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 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 S-arithmetic subgroups in the number field case.

F. Grunewald, D. Blasius, J. Franke (1994)

Inventiones mathematicae

Cohomology of the boundary of Siegel modular varieties of degree two, with applications

J. William Hoffman, Steven H. Weintraub (2003)

Fundamenta Mathematicae

Let 𝓐₂(n) = Γ₂(n)∖𝔖₂ be the quotient of Siegel's space of degree 2 by the principal congruence subgroup of level n in Sp(4,ℤ). This is the moduli space of principally polarized abelian surfaces with a level n structure. Let 𝓐₂(n)* denote the Igusa compactification of this space, and ∂𝓐₂(n)* = 𝓐₂(n)* - 𝓐₂(n) its "boundary". This is a divisor with normal crossings. The main result of this paper is the determination of H(∂𝓐₂(n)*) as a module over the finite group Γ₂(1)/Γ₂(n). As an application...

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Cohomologie des espaces de formes automorphes

Cohomologie des fonctions $_{0} F_{n}$

Cohomologie d’intersection et fonctions $L$ de certaines variétés de Shimura

Cohomologie galoisienne : progrès et problèmes

Cohomologie, $L$ -groupes et fonctorialité

Cohomology groups of the class groups over a ℤₚ extension

Cohomology groups of units in $ℤ_{p}^{d}$ -extensions

Cohomology of arithmetic groups and congruences between systems of Hecke eigenvalues.

Cohomology of arithmetic groups with infinite dimensional coefficient spaces.

Cohomology of arithmetic subgroups of SL3 at infinity.

Cohomology of Drinfeld symmetric spaces and Harmonic cochains

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

Cohomology of S-arithmetic subgroups in the number field case.

Cohomology of the boundary of Siegel modular varieties of degree two, with applications

Cohomology of torus bundles over Kuga fiber varieties.

Cohomology of Vector-Valued Automorphic Forms.

Cohomology sets inside arithmetic groups

Coincidences in the values of the Euler and Carmichael functions

Coleman power series for $K_{2}$ and $p$ -adic zeta functions of modular forms.

Collatz cycles with few descents

Currently displaying 261 – 280 of 906