Diophantine geometry over groups I : Makanin-Razborov diagrams
Publications Mathématiques de l'IHÉS, Tome 93 (2001) , pp. 31-105.

This paper is the first in a sequence on the structure of sets of solutions to systems of equations in a free group, projections of such sets, and the structure of elementary sets defined over a free group. In the first paper we present the (canonical) Makanin-Razborov diagram that encodes the set of solutions of a system of equations. We continue by studying parametric families of sets of solutions, and associate with such a family a canonical graded Makanin-Razborov diagram, that encodes the collection of Makanin-Razborov diagrams associated with the individual members in the parametric family.

@article{PMIHES_2001__93__31_0,
author = {Sela, Zlil},
title = {Diophantine geometry over groups I : Makanin-Razborov diagrams},
journal = {Publications Math\'ematiques de l'IH\'ES},
pages = {31--105},
publisher = {Institut des Hautes \'Etudes Scientifiques},
volume = {93},
year = {2001},
zbl = {1018.20034},
mrnumber = {1863735},
language = {en},
url = {http://www.numdam.org/item/PMIHES_2001__93__31_0/}
}
Sela, Zlil. Diophantine geometry over groups I : Makanin-Razborov diagrams. Publications Mathématiques de l'IHÉS, Tome 93 (2001) , pp. 31-105. http://www.numdam.org/item/PMIHES_2001__93__31_0/

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