An analogue of the field-of-norms functor and of the Grothendieck conjecture-Reference-Cited by-同舟云学术

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

Published:2007-05-23 Issue:4 Volume:16 Page:671-730
ISSN:1056-3911
Container-title:Journal of Algebraic Geometry
language:en
Short-container-title:J. Algebraic Geom.

Author:

Abrashkin Victor

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 p case, which was proved earlier by the author.

Publisher

American Mathematical Society (AMS)

Subject

Geometry and Topology,Algebra and Number Theory

Reference27 articles.

1. Galois modules of group schemes of period 𝑝 over the ring of Witt vectors;Abrashkin, V. A.;Izv. Akad. Nauk SSSR Ser. Mat.,1987

2. The field of norms functor and the Brückner-Vostokov formula;Abrashkin, Victor A.;Math. Ann.,1997

3. Explicit formulas for the Hilbert symbol of a formal group over Witt vectors;Abrashkin, V. A.;Izv. Ross. Akad. Nauk Ser. Mat.,1997

4. On a local analogue of the Grothendieck conjecture;Abrashkin, Victor A.;Internat. J. Math.,2000

5. Ramification theory for higher dimensional local fields;Abrashkin, Victor,2002

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