An explicit formula for the Hilbert symbol of a formal group

Details An explicit formula for the Hilbert symbol of a formal group An explicit formula for the Hilbert symbol of a formal group

2008-11-19

arxiv.org/abs/0811.3132v1

Mathematics

Number Theory

73 pages

Scientific paper

Abrashkin established the Bruckner-Vostokov formula for the Hilbert symbol of a formal group under the assumption that roots of unity belong to the base field. The main motivation of this work is to remove this hypothesis. It is obtained by combining methods of ($\varphi, \Gamma$)-modules and a cohomological interpretation of Abrashkin's technique. To do this, we build ($\varphi, \Gamma$)-modules adapted to the false Tate curve extension and generalize some related tools like the Herr complex with explicit formulas for the cup-product and the Kummer map.

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