Infinitesimal criterion for flatness of projective morphism of schemes
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N. V. Timofeeva
Translated by: the author - St. Petersburg Math. J. 26 (2015), 131-138
- DOI: https://doi.org/10.1090/S1061-0022-2014-01334-9
- Published electronically: November 21, 2014
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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
- Robin Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York-Heidelberg, 1977. MR 0463157
- James S. Milne, Étale cohomology, Princeton Mathematical Series, No. 33, Princeton University Press, Princeton, N.J., 1980. MR 559531
- 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
- M. F. Atiyah and I. G. Macdonald, Introduction to commutative algebra, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969. MR 0242802
Bibliographic Information
- N. V. Timofeeva
- Affiliation: Yaroslavl′ State University, Sovetskaya str. 14, Yaroslavl′150000, Russia
- Email: ntimofeeva@list.ru
- 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.
- © Copyright 2014 American Mathematical Society
- Journal: St. Petersburg Math. J. 26 (2015), 131-138
- MSC (2010): Primary 14B25; Secondary 13D10, 14A15
- DOI: https://doi.org/10.1090/S1061-0022-2014-01334-9
- MathSciNet review: 3234808