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.
Author partially supported by NSF grants DMS-9306159, DMS-9626856 and INT-9224546, and an AMS Centennial Fellowship.
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© 1998 Springer-Verlag Berlin Heidelberg
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Marker, D. (1998). Zariski geometries. In: Bouscaren, E. (eds) Model Theory and Algebraic Geometry. Lecture Notes in Mathematics, vol 1696. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68521-0_7
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DOI: https://doi.org/10.1007/978-3-540-68521-0_7
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