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}, mrnumber = {1863735}, zbl = {1018.20034}, language = {en}, url = {http://archive.numdam.org/item/PMIHES_2001__93__31_0/} }
TY - JOUR AU - Sela, Zlil TI - Diophantine geometry over groups I : Makanin-Razborov diagrams JO - Publications Mathématiques de l'IHÉS PY - 2001 SP - 31 EP - 105 VL - 93 PB - Institut des Hautes Études Scientifiques UR - http://archive.numdam.org/item/PMIHES_2001__93__31_0/ LA - en ID - PMIHES_2001__93__31_0 ER -
Sela, Zlil. Diophantine geometry over groups I : Makanin-Razborov diagrams. Publications Mathématiques de l'IHÉS, Tome 93 (2001), pp. 31-105. http://archive.numdam.org/item/PMIHES_2001__93__31_0/
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