Essential dimension: A functorial point of view (after A. Merkurjev).
Berhuy, Grégory, Favi, Giordano (2003)
Documenta Mathematica
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Berhuy, Grégory, Favi, Giordano (2003)
Documenta Mathematica
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Marco Antei (2010)
Journal de Théorie des Nombres de Bordeaux
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We show that the natural morphism between the fundamental group scheme of the generic fiber of a scheme over a connected Dedekind scheme and the generic fiber of the fundamental group scheme of is always faithfully flat. As an application we give a necessary and sufficient condition for a finite, dominated pointed -torsor over to be extended over . We finally provide examples where is an isomorphism.
Kunz, Ernst, Waldi, Rolf (2007)
Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
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Victor Abrashkin, Ruth Jenni (2012)
Journal de Théorie des Nombres de Bordeaux
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The field-of-norms functor is applied to deduce an explicit formula for the Hilbert symbol in the mixed characteristic case from the explicit formula for the Witt symbol in characteristic in the context of higher local fields. Is is shown that a “very special case” of this construction gives Vostokov’s explicit formula.
Sandrine Jean (2009)
Journal de Théorie des Nombres de Bordeaux
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Let be the algebraic closure of and be the local field of formal power series with coefficients in . The aim of this paper is the description of the set of conjugacy classes of series of order for the composition law. This work is concerned with the formal power series with coefficients in a field of characteristic which are invertible and of finite order for the composition law. In order to investigate Oort’s conjecture, I give a description of conjugacy classes of series...
Kevin Keating (2009)
Journal de Théorie des Nombres de Bordeaux
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Let be a finite field. Wintenberger used the field of norms to give an equivalence between a category whose objects are totally ramified abelian -adic Lie extensions , where is a local field with residue field , and a category whose objects are pairs , where and is an abelian -adic Lie subgroup of . In this paper we extend this equivalence to allow and to be arbitrary abelian pro- groups.