|
Zariski geometries
Author(s):
Ehud
Hrushovski;
Boris
Zilber
Journal:
J. Amer. Math. Soc.
9
(1996),
1-56.
MSC (1991):
Primary 03C68, 14A99;
Secondary 03C65, 14E10
Retrieve article in:
PDF DVI PostScript
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
A characterization is obtained of the Zariski topology over an algebraically closed field.
References:
- AE
- E. Artin, Geometric algebra, Interscience, New York, 1957; Springer-Verlag, Berlin and New York, 1988. MR 90h:51003
- AM
- M. Artin, Algebraic spaces, Yale University, 1969. MR 53:10795
- B
- E. Bouscaren, Hrushovski's group configuration, The Model Theory of Groups (A. Nesin and A. Pillay, eds.), Notre Dame Math. Lectures, no. 11, Univ. Notre Dame Press, Notre Dame, IN, 1989. CMP 21:09
- BL
- T. J. Baldwin and A. Lachlan, On strongly minimal sets, J. Symbolic Logic 36 1971, 79--96. MR 44:3851
- Ch
- G. Cherlin, Groups of small Morley rank, Ann. of Math. Logic 17, 1979, 1--28. MR 81h:03072
- CK
- C. C. Chang and H. J. Keisler, Model theory, North-Holland, Amsterdam, 1973. MR 53:12927
- EH
- D. Evans and E. Hrushovksi, Projective planes in algebraically closed fields, Proc. London Math. Soc. (3) 62, 1991, 1--24. MR 92a:05031
- FJ
- M. Fried and M. Jarden, Field arithmetic, Springer-Verlag, Berlin, 1986. MR 89b:12010
- GH
- P. Griffiths and J. Harris, Principles of algebraic geometry, Wiley-Interscience, New York, 1978. MR 80b:14001
- Ha
- R. Hartshorne, Algebraic geometry, Springer, New York, 1977. MR 57:3116
- HH
- V. Harnik and L. Harrington, Fundamentals of forking, Ann. Pure Appl. Logic 26, (1984). MR 86c:03032
- 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-Amsterdam, 1987. MR 88e:03051
- Hr1
- E. Hrushovski, Unimodular minimal structures, J. London Math. Soc. (2) 46, (1992), 385--396. MR 94b:03062
- Hr2
- ------, Locally modular regular types, Classification Theory (Chicago 1985) (J. T. Baldwin, ed.), Springer-Verlag, Berlin and New York, 1987. MR 90m:03064
- Hr3
- ------, A new strongly minimal set, Ann. Pure Appl. Logic 62, (1993), 147--166. MR 94d:03064
- Hr4
- ------, Strongly minimal expansions of algebraically closed fields, Israel J. Math. 79, (1992), 129--151. MR 95c:03078
- Hr5
- ------ Recognizing groups in homogeneous geometries, preprint.
- Hr6
- ------ Almost orthogonal regular types, Ann. Pure Appl. Logic 45, (1989), 139--155. MR 91k:03083
- Hr7
- ------ Kueker's conjecture for stable theories, J. Symbolic Logic 54, (1989), 221--225. MR 90b:03046
- HZ
- E. Hrushovski and B. Zilber, Zariski geometries, Bull. Amer. Math. Soc. (N.S.) 28, (1993), 315--323. MR 93j:14003
- L
- S. Lang, Introduction to algebraic geometry, Interscience, New York, 1964. MR 20:7021
- Ma
- A. Macintyre, On aleph-one categorical theories of fields, Fund. Math. 71, (1971), 1--25. MR 45:48
- Mo
- M. Morley, Categoricity in power, Trans. Amer. Math. Soc. 114, (1965), 514--538. MR 31:58
- Pi1
- A. Pillay, An introduction to stability theory, Oxford Univ. Press, London and New York, 1983. MR 85i:03104
- Pi2
- Anand Pillay (forthcoming),
- Po
- Bruno Poizat, Missionary mathematics, J. Symbolic Logic 53, (1988), 137--145. MR 89b:03058
- W
- A. Weil, On algebraic groups of transformations, Amer. J. Math. 77, (1955), 355--391. MR 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 87d:03093b
Similar Articles:
Retrieve articles in Journal of the American Mathematical Society
with MSC
(1991):
03C68, 14A99,
03C65, 14E10
Retrieve articles in all Journals with MSC
(1991):
03C68, 14A99,
03C65, 14E10
Additional Information:
Ehud
Hrushovski
Affiliation:
Department of Mathematics, Hebrew University, Jerusalem, Israel
Email:
ehud@sunset.ma.huji.ac.il
Boris
Zilber
Affiliation:
Department of Mathematics, Kemerovo University, Kemerovo, Russia
DOI:
10.1090/S0894-0347-96-00180-4
PII:
S 0894-0347(96)00180-4
Received by editor(s):
November 11, 1992
Received by editor(s) in revised form:
September 1, 1993
Additional Notes:
The first author was supported by National Science Foundation grant 9106711-DMS
Copyright of article:
Copyright
1996,
American Mathematical Society
|
Comments: webmaster@ams.org