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A dimension formula for Ekedahl-Oort strata

Ben Moonen (2004)

Annales de l’institut Fourier

We study the Ekedahl-Oort stratification on moduli spaces of PEL type. The strata are indexed by the classes in a Weyl group modulo a subgroup, and each class has a distinguished representative of minimal length. The main result of this paper is that the dimension of a stratum equals the length of the corresponding Weyl group element. We also discuss some explicit examples.

A note on certain Tannakian group schemes

Sanjay Amrutiya (2020)

Archivum Mathematicum

In this note, we prove that the F -fundamental group scheme is a birational invariant for smooth projective varieties. We prove that the F -fundamental group scheme is naturally a quotient of the Nori fundamental group scheme. For elliptic curves, it turns out that the F -fundamental group scheme and the Nori fundamental group scheme coincide. We also consider an extension of the Nori fundamental group scheme in positive characteristic using semi-essentially finite vector bundles, and prove that in...

Bruhat-Tits theory from Berkovich’s point of view. I. Realizations and compactifications of buildings

Bertrand Rémy, Amaury Thuillier, Annette Werner (2010)

Annales scientifiques de l'École Normale Supérieure

We investigate Bruhat-Tits buildings and their compactifications by means of Berkovich analytic geometry over complete non-Archimedean fields. For every reductive group G over a suitable non-Archimedean field k we define a map from the Bruhat-Tits building ℬ ( G , k ) to the Berkovich analytic space G an associated with G . Composing this map with the projection of G an to its flag varieties, we define a family of compactifications of ℬ ( G , k ) . This generalizes results by Berkovich in the case of split groups. Moreover,...

Cohomologial dimension of Laumon 1-motives up to isogenies

Nicola Mazzari (2010)

Journal de Théorie des Nombres de Bordeaux

We prove that the category of Laumon 1-motives up to isogenies over a field of characteristic zero is of cohomological dimension ≤ 1 . As a consequence this implies the same result for the category of formal Hodge structures of level ≤ 1 (over ℚ ).

Comparison between the fundamental group scheme of a relative scheme and that of its generic fiber

Marco Antei (2010)

Journal de Théorie des Nombres de Bordeaux

We show that the natural morphism ϕ : π 1 ( X η , x η ) → π 1 ( X , x ) η between the fundamental group scheme of the generic fiber X η of a scheme X over a connected Dedekind scheme and the generic fiber of the fundamental group scheme of X is always faithfully flat. As an application we give a necessary and sufficient condition for a finite, dominated pointed G -torsor over X η to be extended over X . We finally provide examples where ϕ : π 1 ( X η , x η ) → π 1 ( X , x ) η is an isomorphism.

Contractions of Lie algebras and algebraic groups

Dietrich Burde (2007)

Archivum Mathematicum

Degenerations, contractions and deformations of various algebraic structures play an important role in mathematics and physics. There are many different definitions and special cases of these notions. We try to give a general definition which unifies these notions and shows the connections among them. Here we focus on contractions of Lie algebras and algebraic groups.

Correspondencias divisoriales entre esquemas relativos.

Daniel Hernández Ruipérez (1981)

Revista Matemática Hispanoamericana

En este trabajo se estudian las correspondencias divisoriales entre dos esquemas relativos. Una correspondencia divisorial es una correspondencia algebraica entre los puntos de un esquema X y las clases de equivalencia lineal de divisores de otro esquema Y. Se consideran correspondencias triviales las que asignan a cada punto toda la variedad y las inversas de éstas. Por tanto las correspondencias divisoriales módulo las triviales son los divisores del producto módulo, módulo los divisores que provienen...

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