Additive structure of multiplicative subgroups of fields and Galois theory
Louis Mahé
Institut de recherche mathématique de Rennes, FranceTara L. Smith
Sciences Univ. of Cincinnati Cincinnati Ohio 45221-0025 U.S.AJán Mináč
Western University, London, Canada

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.
Cite this article
Louis Mahé, Tara L. Smith, Ján Mináč, Additive structure of multiplicative subgroups of fields and Galois theory. Doc. Math. 9 (2004), pp. 301–355
DOI 10.4171/DM/169