Realising the cup product of local Tate duality
Rachel Newton1
1 Max-Planck-Institut für Mathematik Vivatsgasse 7 53111 Bonn Germany
Journal de théorie des nombres de Bordeaux, Volume 27 (2015) no. 1, pp. 219-244.

We present an explicit description, in terms of central simple algebras, of a cup product map which occurs in the statement of local Tate duality for Galois modules of prime cardinality p. Given cocycles f and g, we construct a central simple algebra of dimension p 2 whose class in the Brauer group gives the cup product f∪g. This algebra is as small as possible.

Nous présentons une description explicite, en termes d’algèbres centrales simples, d’un cup-produit intervenant dans l’énoncé de la dualité de Tate locale pour les modules galoisiens d’ordre premier p. Étant donnés deux cocycles f et g, nous construisons une algèbre centrale simple de dimension p 2 dont la classe dans le groupe de Brauer donne le cup-produit f∪g. Cette algèbre est aussi petite que possible.

DOI: 10.5802/jtnb.900
Classification: 16K20, 12G05
Rachel Newton 1

1 Max-Planck-Institut für Mathematik Vivatsgasse 7 53111 Bonn Germany 
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Rachel Newton. Realising the cup product of  local Tate duality. Journal de théorie des nombres de Bordeaux, Volume 27 (2015) no. 1, pp. 219-244. doi : 10.5802/jtnb.900. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.900/

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