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Zariski geometries

  • David Marker
Part of the Lecture Notes in Mathematics book series (LNM, volume 1696)

Abstract

Zariski geometries were introduced by Hrushovski and Zilber in [HrZi 96], [HrZi 93] and [Zil]. From a technical point of view this work provides a class of strongly minimal sets where Zilber’s conjecture holds (see [Zie, end of section 5]. It also provides the answer to two metamathematical questions. How do you characterize the topological spaces that arise from the Zariski topology of an algebraic curve? Can you recover the field from the topological spaces? The answer to these questions is provided by Theorem 3.3 below. This result plays a key role in Hrushovski’s proof of the Mordell-Lang conjecture for function fields.

Keywords

Irreducible Component Algebraic Curve Transcendence Degree Zariski Topology Quantifier Elimination 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • David Marker
    • 1
  1. 1.Department of MathematicsUniversity of Illinois at ChicagoChicagoUSA

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