Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Modified proof of a local analogue of the Grothendieck conjecture   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.

35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn