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REFINED SWAN CONDUCTORS $\text{mod}~p$ OF ONE-DIMENSIONAL GALOIS REPRESENTATIONS

Part of: Algebraic number theory: local and $p$-adic fields (Co)homology theory

Published online by Cambridge University Press:  03 June 2019

KAZUYA KATO ,
ISABEL LEAL  and
TAKESHI SAITO
KAZUYA KATO
Affiliation:
Department of Mathematics, University of Chicago, Chicago, Illinois 60637, USA email kkato@math.uchicago.edu
ISABEL LEAL
Affiliation:
Courant Institute of Mathematical Sciences, New York, NY 10012-1185, USA email leal@courant.nyu.edu
TAKESHI SAITO
Affiliation:
Department of Mathematical Sciences, University of Tokyo, Komaba, Meguro, Tokyo 153-8914, Japan email t-saito@ms.u-tokyo.ac.jp
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Abstract

For a character of the absolute Galois group of a complete discrete valuation field, we define a lifting of the refined Swan conductor, using higher dimensional class field theory.

MSC classification

Primary: 14F30: $p$-adic cohomology, crystalline cohomology 11S31: Class field theory; $p$-adic formal groups
Type
Article
Information
Nagoya Mathematical Journal , Volume 236: Celebrating the 60th Birthday of Shuji Saito , December 2019 , pp. 134 - 182
Copyright
© 2019 Foundation Nagoya Mathematical Journal  

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Footnotes

One of the authors (K.K.) is partially supported by NSF Award 1601861 and (T.S.) is partially supported by JSPS Grant-in-Aid for Scientific Research (A) 26247002.

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