Additive structure of multiplicative subgroups of fields and Galois theory
Group Theory
2007-05-23 v1
Abstract
One of the fundamental questions in current field theory, related to Grothendieck's conjecture of birational anabelian geometry, is the investigation of the precise relationship between the Galois theory of fields and the structure of the fields themselves. In this paper we initiate the classification of additive properties of multiplicative subgroups of fields containing all squares, using pro-2-Galois groups of nilpotency class at most 2, and of exponent at most 4. This work extends some powerful methods and techniques from formally real fields to general fields of characteristic not 2.
Keywords
Cite
@article{arxiv.math/0110283,
title = {Additive structure of multiplicative subgroups of fields and Galois theory},
author = {Louis Mahé and Ján Mináč and Tara L. Smith},
journal= {arXiv preprint arXiv:math/0110283},
year = {2007}
}