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arXiv · 0907.3035

Modified proof of a local analogue of the Grothendieck conjecture

Victor Abrashkin
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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 $p\ne 0$ and the category of absolute Galois groups of fields $K$ together with their ramification filtrations. The case of characteristic 0 fields $K$ was considered by Mochizuki several years ago. Then the author proved it by different method if $p>2$ (but $\operatorname{char}K=0$ or $p$). This paper represents a modified approach: it covers the case $p=2$, contains considerable technical simplifications and replaces the Galois group of $K$ by its maximal pro-$p$-quotient. Special attention is paid to the procedure of recovering field isomorphisms coming from isomorphisms of Galois groups, which are compatible with the corresponding ramification filtrations.

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Victor Abrashkin. 2009-07-17. Modified proof of a local analogue of the Grothendieck conjecture. https://arxiv.org/abs/0907.3035

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