Cohomology groups of units in -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
Let be a non-archimedean local field. This paper gives an explicit isomorphism between the dual of the special representation of and the space of harmonic cochains defined on the Bruhat-Tits building of , 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 -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
Let be a prime and let be a -group of matrices in , for some integer . In this paper we show that, when , a certain subgroup of the cohomology group is trivial. We also show that this statement can be false when . Together with a result of Dvornicich and Zannier (see [2]), we obtain that any algebraic torus of dimension enjoys a local-global principle on divisibility by .
Cohomology of S-arithmetic subgroups in the number field case.
Cohomology of the boundary of Siegel modular varieties of degree two, with applications
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...
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 and -adic zeta functions of modular forms.
Collatz cycles with few descents
Combinatoire de mots récurrents de complexité n+2
Nous établissons quelques propriétés des mots sturmiens et classifions, ensuite, les mots infinis qui possèdent, pour tout entier naturel non nul n, exactement n+2 facteurs de longueur n. Nous définissons également la notion d'insertion k à k sur les mots infinis puis nous calculons la complexité des mots obtenus en appliquant cette notion aux mots sturmiens. Enfin nous étudions l'équilibre et la palindromie d'une classe particulière de mots de complexité n+2 que nous appelons mots quasi-sturmiens...
Combinatoire des arbres planaires et arithmétique des courbes hyperelliptiques
Le but de cet article est de proposer une nouvelle méthode pour des études dans le cadre de la théorie des “dessins d’enfants” de A. Grothendieck de certaines questions concernant l’action du groupe de Galois absolu sur l’ensemble des arbres planaires.On définit l’application qui associe à chaque arbre planaire à arêtes, une courbe hyperelliptique avec un point de -division. Cette construction permet d’établir un lien entre la théorie de la torsion des courbes hyperelliptiques et celle des “dessins...
Combinatoire des codages de rotations
Combinatoire du billard dans un polyèdre
Ces notes ont pour but de rassembler les différents résultats de combinatoire des mots relatifs au billard polygonal et polyédral. On commence par rappeler quelques notions de combinatoire, puis on définit le billard, les notions utiles en dynamique et le codage de l’application. On énonce alors les résultats connus en dimension deux puis trois.
Combinatorial and arithmetical properties of infinite words associated with non-simple quadratic Parry numbers
We study some arithmetical and combinatorial properties of β-integers for β being the larger root of the equation x2 = mx - n,m,n ∈ ℵ, m ≥ n +2 ≥ 3. We determine with the accuracy of ± 1 the maximal number of β-fractional positions, which may arise as a result of addition of two β-integers. For the infinite word uβ> coding distances between the consecutive β-integers, we determine precisely also the balance. The word uβ> is the only fixed point of the morphism A → Am-1B and B → Am-n-1B. In...
Combinatorial aspects of elliptic curves.