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Infinitesimal criterion for flatness of projective morphism of schemes

Author: N. V. Timofeeva
Translated by: the author
Original publication: Algebra i Analiz, tom 26 (2014), nomer 1.
Journal: St. Petersburg Math. J. 26 (2015), 131-138
MSC (2010): Primary 14B25; Secondary 13D10, 14A15
Published electronically: November 21, 2014
MathSciNet review: 3234808
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Abstract | References | Similar Articles | Additional Information

Abstract: A generalization of the well-known criterion for flatness of a projective morphism of Noetherian schemes involving the Hilbert polynomial is given for the case of a nonreduced base of the morphism.

References [Enhancements On Off] (What's this?)

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  • 2. James S. Milne, Étale cohomology, Princeton Mathematical Series, vol. 33, Princeton University Press, Princeton, N.J., 1980. MR 559531
  • 3. Hideyuki Matsumura, Commutative ring theory, Cambridge Studies in Advanced Mathematics, vol. 8, Cambridge University Press, Cambridge, 1986. Translated from the Japanese by M. Reid. MR 879273
  • 4. M. F. Atiyah and I. G. Macdonald, Introduction to commutative algebra, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969. MR 0242802

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Additional Information

N. V. Timofeeva
Affiliation: Yaroslavl′ State University, Sovetskaya str. 14, Yaroslavl′150000, Russia

Keywords: Noetherian algebraic schemes, projective morphism, nonreduced scheme structure, flat morphism, coherent sheaf of modules
Received by editor(s): December 18, 2012
Published electronically: November 21, 2014
Additional Notes: The author was partially supported by the Institute of Mathematics “Simion Stoilow” of Romanian Academy (IMAR) (partnership IMAR – BITDEFENDER) during the author’s stay as invited professor, June – July 2011.
Article copyright: © Copyright 2014 American Mathematical Society