Additive structure of multiplicative subgroups of fields and Galois theory

Details Additive structure of multiplicative subgroups of fields and Galois theory Additive structure of multiplicative subgroups of fields and Galois theory

2001-10-25

arxiv.org/abs/math/0110283v1

Mathematics

Group Theory

Scientific paper

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.

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