Displaying similar documents to “Universal covering spaces and fundamental groups in algebraic geometry as schemes”

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

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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.

The fundamental groupoid scheme and applications

Hélène Esnault, Phùng Hô Hai (2008)

Annales de l’institut Fourier

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We define a linear structure on Grothendieck’s arithmetic fundamental group π 1 ( X , x ) of a scheme X defined over a field k of characteristic 0. It allows us to link the existence of sections of the Galois group Gal ( k ¯ / k ) to π 1 ( X , x ) with the existence of a neutral fiber functor on the category which linearizes it. We apply the construction to affine curves and neutral fiber functors coming from a tangent vector at a rational point at infinity, in order to follow this rational point in the universal covering...

A topological version of Bertini's theorem

Artur Piękosz (1995)

Annales Polonici Mathematici

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We give a topological version of a Bertini type theorem due to Abhyankar. A new definition of a branched covering is given. If the restriction π V : V → Y of the natural projection π: Y × Z → Y to a closed set V ⊂ Y × Z is a branched covering then, under certain assumptions, we can obtain generators of the fundamental group π₁((Y×Z).

On the disc theorem

Cabiria Andreian Cazacu (1991)

Annales Polonici Mathematici

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Ahlfors' disc theorem for Riemann covering surfaces is extended to normally exhaustible Klein coverings.

Braid Monodromy of Algebraic Curves

José Ignacio Cogolludo-Agustín (2011)

Annales mathématiques Blaise Pascal

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These are the notes from a one-week course on Braid Monodromy of Algebraic Curves given at the Université de Pau et des Pays de l’Adour during the Première Ecole Franco-Espagnole: Groupes de tresses et topologie en petite dimension in October 2009. This is intended to be an introductory survey through which we hope we can briefly outline the power of the concept monodromy as a common area for group theory, algebraic geometry, and topology of projective...

Realization of primitive branched coverings over closed surfaces following the hurwitz approach

Semeon Bogatyi, Daciberg Gonçalves, Elena Kudryavtseva, Heiner Zieschang (2003)

Open Mathematics

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Let V be a closed surface, H⊑π1(V) a subgroup of finite index l and D=[A 1,...,A m] a collection of partitions of a given number d≥2 with positive defect v(D). When does there exist a connected branched covering f:W→V of order d with branch data D and f∶W→V It has been shown by geometric arguments [4] that, for l=1 and a surface V different from the sphere and the projective plane, the corresponding branched covering exists (the data D is realizable) if and only if the data D fulfills...

Local ε 0 -characters in torsion rings

Seidai Yasuda (2007)

Journal de Théorie des Nombres de Bordeaux

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Let p be a rational prime and K a complete discrete valuation field with residue field k of positive characteristic p . When k is finite, generalizing the theory of Deligne [], we construct in [] and [] a theory of local ε 0 -constants for representations, over a complete local ring with an algebraically closed residue field of characteristic ≠ p , of the Weil group W K of K . In this paper, we generalize the results in [] and [] to the case where k is an arbitrary perfect field.