Displaying similar documents to “A class–field theoretical calculation”

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

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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 prime order ones of the π 1 ( ℳ 0 , [ n ] ) .

Classification of self-dual torsion-free LCA groups

S. Wu (1992)

Fundamenta Mathematicae

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In this paper we seek to describe the structure of self-dual torsion-free LCA groups. We first present a proof of the structure theorem of self-dual torsion-free metric LCA groups. Then we generalize the structure theorem to a larger class of self-dual torsion-free LCA groups. We also give a characterization of torsion-free divisible LCA groups. Consequently, a complete classification of self-dual divisible LCA groups is obtained; and any self-dual torsion-free LCA group can be regarded...

Some remarks on almost rational torsion points

John Boxall, David Grant (2006)

Journal de Théorie des Nombres de Bordeaux

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For a commutative algebraic group G over a perfect field k , Ribet defined the set of almost rational torsion points G tors , k ar of G over k . For positive integers d , g , we show there is an integer U d , g such that for all tori T of dimension at most d over number fields of degree at most g , T tors , k ar ⊆ T [ U d , g ] . We show the corresponding result for abelian varieties with complex multiplication, and under an additional hypothesis, for elliptic curves without complex multiplication. Finally, we show that except for an explicit...

An introduction to the abelian Reidemeister torsion of three-dimensional manifolds

Gwénaël Massuyeau (2011)

Annales mathématiques Blaise Pascal

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These notes accompany some lectures given at the autumn school “” in October 2009. The abelian Reidemeister torsion for 3 -manifolds, and its refinements by Turaev, are introduced. Some applications, including relations between the Reidemeister torsion and other classical invariants, are surveyed.