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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A short proof of Castelnuovo's criterion of rationality


Author: William E. Lang
Journal: Trans. Amer. Math. Soc. 264 (1981), 579-582
MSC: Primary 14J10; Secondary 14E30, 14F30
MathSciNet review: 603783
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Abstract: We give a new proof in positive characteristic of Castelnuovo's criterion of rationality of algebraic surfaces. We use crystalline cohomology and the de Rham-Witt complex as a substitute for the transcendeal methods of Kodaira.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1981-0603783-3
PII: S 0002-9947(1981)0603783-3
Keywords: Algebraic surface, crystalline cohomology, de Rham-Witt complex, rational double point, Brieskorn resolution, elliptic surface
Article copyright: © Copyright 1981 American Mathematical Society