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On Totally Ramified Extensions of Discrete Valued Fields

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Arithmetic and Geometry Around Galois Theory

Part of the book series: Progress in Mathematics ((PM,volume 304))

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Abstract

We give a simple characterization of the totally wild ramified valuations in a Galois extension of fields of characteristic p. This criterion involves the valuations of Artin‐Schreier cosets of the 𝔽×pr̵translation of a single element. We apply the criterion to construct some interesting examples.

Mathematics Subject Classification (2010).12G10.

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Authors and Affiliations

  1. Einstein Institute of Mathematics Edmond J. Safra Campus Givat Ram, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel

    Lior Bary-Soroker

  2. School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv, 69978, Israel

    Elad Paran

Authors
  1. Lior Bary-Soroker
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  2. Elad Paran
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Corresponding author

Correspondence to Lior Bary-Soroker .

Editor information

Editors and Affiliations

  1. , Laboratoire Paul Painlevé, Université Lille 1, Cité Scientifique, Villeneuve d'Ascq Cédex, 59655, France

    Pierre Dèbes

  2. , Laboratoire Paul Painlevé, Université Lille 1, Cité Scientifique, Villeneuve d'Ascq Cédex, 59655, France

    Michel Emsalem

  3. , Institut de Recherche Mathématique de Re, Université Rennes 1, Campus de Beaulieu, Rennes Cedex, 35042, France

    Matthieu Romagny

  4. , Department of Mathematics, Galatasaray University, Cırağan Cad. 36, Beşiktaş, İstanbul, 34357, Turkey

    A. Muhammed Uludağ

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Bary-Soroker, L., Paran, E. (2013). On Totally Ramified Extensions of Discrete Valued Fields. In: Dèbes, P., Emsalem, M., Romagny, M., Uludağ, A. (eds) Arithmetic and Geometry Around Galois Theory. Progress in Mathematics, vol 304. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0487-5_9

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