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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Algorithmic proof of the epsilon constant conjecture


Authors: Werner Bley and Ruben Debeerst
Journal: Math. Comp. 82 (2013), 2363-2387
MSC (2010): Primary 11Y40; Secondary 11R33, 11S25
Published electronically: April 1, 2013
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Abstract: In this paper we will algorithmically prove the global epsilon constant conjecture for all Galois extensions $ L/\mathbb{Q}$ of degree at most $ 15$. In fact, we will obtain a slightly more general result whose proof is based on an algorithmic proof of the local epsilon constant conjecture for Galois extensions $ E/\mathbb{Q}_p$ of small degree. To this end we will present an efficient algorithm for the computation of local fundamental classes and address several other problems arising in the algorithmic proof of the local conjecture.


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Additional Information

Werner Bley
Affiliation: Universität München, Theresienstr. 39, 80333 München, Germany
Email: bley@math.lmu.de

Ruben Debeerst
Affiliation: Universität Kassel, Heinrich-Plett-Str. 40, 34132 Kassel, Germany
Address at time of publication: Heidelberger Landstraße 101B, 64 297 Darmstadt, Germany
Email: ruben.debeerst@gmx.de

DOI: http://dx.doi.org/10.1090/S0025-5718-2013-02691-9
PII: S 0025-5718(2013)02691-9
Keywords: Epsilon constant conjecture, local fundamental classes
Received by editor(s): October 7, 2011
Received by editor(s) in revised form: February 23, 2012
Published electronically: April 1, 2013
Additional Notes: The second author was supported by DFG grant BL 395/3-1
Article copyright: © Copyright 2013 American Mathematical Society