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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)



Zariski geometries

Authors: Ehud Hrushovski and Boris Zilber
Journal: Bull. Amer. Math. Soc. 28 (1993), 315-323
MSC: Primary 14A99; Secondary 03C45, 03C60, 03C65, 14H99
MathSciNet review: 1183999
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Abstract: We characterize the Zariski topologies over an algebraically closed field in terms of general dimension-theoretic properties. Some applications are given to complex manifold and to strongly minimal sets.

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  • [A] M. Artin, Algebraic spaces, Yale University Press, New Haven, CT, 1969. MR 0407012 (53:10795)
  • [BL] T. J. Baldwin and A. Lachlan, On strongly minimal sets, Symbolic Logic 36 (1971), 79-96. MR 0286642 (44:3851)
  • [CK] C. C. Chang and H. J. Keisler, Model theory, North-Holland, Amsterdam, 1973.
  • [EH] D. Evans and E. Hrushovski, Embeddings of matroids infields of prime characteristic, Proc. London Math. Soc. (to appear).
  • [FJ] M. Fried and M. Jarden, Field arithmetic, Springer-Verlag, Berlin, 1986. MR 868860 (89b:12010)
  • [GH] P. Griffiths and J. Harris, Principles of algebraic geometry, Wiley-Interscience, New York, 1978. MR 507725 (80b:14001)
  • [Ha] P. Hartshorne, Algebraic geometry, Springer-Verlag, New York, 1977. MR 0463157 (57:3116)
  • [HL] E. Hrushovski and J. Loveys, Locally modular strongly minimal sets (to appear).
  • [HP] E. Hrushovski and A. Pillay, Weakly normal groups, Logic Colloquium 85 (Paris), North-Holland, Amsterdam, 1986. MR 895647 (88e:03051)
  • [Hr1] E. Hrushovski, A new strongly minimal set, (to appear in Ann. Pure Appl. Logic). MR 1226304 (94d:03064)
  • [Hr2] -, Strongly minimal expansions of algebraically closed fields, Israel J. Math, (to appear.). MR 1248909 (95c:03078)
  • [Mac] A. Macintyre, On aleph-one categorical theories of fields, Fund. Math. 71 (1971), 1-25. MR 0290954 (45:48)
  • [W] A. Weil, On algebraic groups of transformations, Amer. J. Math. 77 (1955), 355-391. MR 0074083 (17:533e)
  • [Z] B. Zilber, The structure of models of uncountably categorical theories, Proc. Internat. Congr. Math. (Warsaw, 1983), vol. 1, North-Holland, Amsterdam, 1984, pp. 359-368. MR 804692 (87d:03093b)

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Article copyright: © Copyright 1993 American Mathematical Society

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