An analogue of the field-of-norms functor and of the Grothendieck conjecture

Abrashkin, Victor

doi:10.1090/S1056-3911-07-00470-5

Author: Victor Abrashkin
Journal: J. Algebraic Geom. 16 (2007), 671-730
DOI: https://doi.org/10.1090/S1056-3911-07-00470-5
Published electronically: May 23, 2007
MathSciNet review: 2357687
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Abstract | References | Additional Information

Abstract: The paper contains a construction of an analogue of the Fontaine-Wintenberger field-of-norms functor for higher-dimensional local fields. This construction is done completely in terms of the ramification theory of such fields. It is applied to deduce the mixed characteristic case of a local analogue of the Grothendieck conjecture for these fields from its characteristic $p$ case, which was proved earlier by the author.

References

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Additional Information

Victor Abrashkin
Affiliation: Department of Mathematics and Sciences, Durham University, Science Laboratories, South Road, Durham, DH1 3LE, United Kingdom
Email: victor.abrashkin@durham.ac.uk

Received by editor(s): September 2, 2005
Received by editor(s) in revised form: October 11, 2006
Published electronically: May 23, 2007