An analogue of the field-of-norms functor and the Grothendieck\n Conjecture

2005/03/10 by Victor Abrashkin, Abrashkin, Victor
Mathematics · #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology #Commutative Algebra and Its Applications

paper · pdf · doi:10.48550/arxiv.math/0503200

Abstract

The paper contains a construction of an analogue of the Fontaine-Wintenberger\nfield-of-norms functor for higher dimensional local fields. This construction\nis done completely in terms of the ramification theory of such fields. It is\napplied to deduce the mixed characteristic case of a local analogue of the\nGrothendieck Conjecture for these fields from its characteristic p case, which\nwas proved earlier by the author.\n

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• Formalizing Norm Extensions and Applications to Number Theory
• Invitation to higher local fields, Part I, section 16: Higher class field theory without using K-groups
• Invitation to higher local fields, Part I, section 17: An approach to higher ramification theory