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Action du groupe de Galois sur les périodes de certaines courbes de Mumford

Christophe Brouillard (1994)

Journal de théorie des nombres de Bordeaux

Nous étudions l’action du groupe de Galois sur les périodes des courbes de Mumford qui sont des revêtements cycliques de ℙ K 1 . Lorsque le degré de ce revêtement est premier à la caractéristique résiduelle du corps de base, nous décomposons le réseau des périodes en une somme directe de modules monogènes, le nombre de ces modules monogènes étant déduit de la géométrie de la courbe (théorème 4). Ceci nous permet de donner une condition nécessaire et suffisante pour que le module des périodes soit libre...

Action of the Grothendieck-Teichmüller group on torsion elements of full Teichmüller modular groups in genus zero

Benjamin Collas (2012)

Journal de Théorie des Nombres de Bordeaux

In this paper we establish the action of the Grothendieck-Teichmüller group G T ^ on the prime order torsion elements of the profinite fundamental group π 1 g e o m ( ℳ 0 , [ n ] ) . As an intermediate result, we prove that the conjugacy classes of prime order torsion of π ^ 1 ( ℳ 0 , [ n ] ) are exactly the discrete prime order ones of the π 1 ( ℳ 0 , [ n ] ) .

Actions of parabolic subgroups in GL_n on unipotent normal subgroups and quasi-hereditary algebras

Thomas Brüstle, Lutz Hille (2000)

Colloquium Mathematicae

Let R be a parabolic subgroup in G L n . It acts on its unipotent radical R u and on any unipotent normal subgroup U via conjugation. Let Λ be the path algebra k t of a directed Dynkin quiver of type with t vertices and B a subbimodule of the radical of Λ viewed as a Λ-bimodule. Each parabolic subgroup R is the group of automorphisms of an algebra Λ(d), which is Morita equivalent to Λ. The action of R on U can be described using matrices over the bimodule B. The advantage of this description is that each...

Adjoint representation of E 8 and del Pezzo surfaces of degree 1

Vera V. Serganova, Alexei N. Skorobogatov (2011)

Annales de l’institut Fourier

Let X be a del Pezzo surface of degree 1 , and let G be the simple Lie group of type E 8 . We construct a locally closed embedding of a universal torsor over X into the G -orbit of the highest weight vector of the adjoint representation. This embedding is equivariant with respect to the action of the Néron-Severi torus T of X identified with a maximal torus of G extended by the group of scalars. Moreover, the T -invariant hyperplane sections of the torsor defined by the roots of G are the inverse images...

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