Modified proof of a local analogue of the Grothendieck Conjecture

Abrashkin, Victor

Abstract

A local analogue of the Grothendieck Conjecture is an equivalence of the category of complete discrete valuation fields K with finite residue fields of characteristic p and the category of their Galois groups together with their ramification filtration. The case of field of characteristic 0 was considered earlier by Mochizuki, the the author proved it by differennt method if p>2, but the characteristic of K is not necessarily 0. This paper represents a modified approach, which covers also the case p=2.

Citation

Abrashkin, V. (2010). Modified proof of a local analogue of the Grothendieck Conjecture. Journal de théorie des nombres de Bordeaux, 22(1), 1-50. https://doi.org/10.5802/jtnb.703

• Journal Article Type: Article
• Publication Date: Jan 1, 2010
• Deposit Date: Feb 21, 2011
• Journal: Journal de théorie des nombres de Bordeaux
• Print ISSN: 1246-7405
• Electronic ISSN: 2118-8572
• Publisher: Institut Mathematiques de Bordeaux
• Peer Reviewed: Peer Reviewed
• Volume: 22
• Issue: 1
• Pages: 1-50
• DOI: https://doi.org/10.5802/jtnb.703
• Keywords: Local fields, Ramification filtration, Grothendieck Conjecture.
• Public URL: https://durham-repository.worktribe.com/output/1512017
• Publisher URL: http://jtnb.cedram.org/jtnb-bin/item?id=JTNB_2010__22_1_1_0