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Diophantine geometry over groups I: Makanin-Razborov diagrams

โœ Scribed by Zlil Sela

Book ID
106300558
Publisher
Springer
Year
2001
Tongue
English
Weight
518 KB
Volume
93
Category
Article
ISSN
0073-8301

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โœฆ Synopsis

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.

๐Ÿ“œ SIMILAR VOLUMES

Algebraic Geometry over Groups I. Algebr
Algebraic Geometry over Groups I. Algebraic Sets and Ideal Theory
โœ Gilbert Baumslag; Alexei Myasnikov; Vladimir Remeslennikov ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 343 KB

The object of this paper, which is the first in a series of three, is to lay the foundations of the theory of ideals and algebraic sets over groups. แฎŠ 1999 Aca- demic Press CONTENTS 1. Introduction. 1.1. Some general comments. 1.2. The category of G-groups. 1.3. Notions from commutative algebra. 1.4