Geodesic
Additive structure of multiplicative subgroups of fields and Galois theory
Documenta mathematica, Tome 9 (2004), pp. 301-355
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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.
DOI : 10.4171/dm/169
Classification : 11E81, 12D15 
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     title = {Additive structure of multiplicative subgroups of fields and {Galois} theory},
     journal = {Documenta mathematica},
     pages = {301--355},
     year = {2004},
     volume = {9},
     doi = {10.4171/dm/169},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/169/}
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Louis Mahé; Tara L. Smith; Ján Mináč. Additive structure of multiplicative subgroups of fields and Galois theory. Documenta mathematica, Tome 9 (2004), pp. 301-355. doi: 10.4171/dm/169

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