On a result of Faltings via tight closure
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- by Tirdad Sharif PDF
- Proc. Amer. Math. Soc. 138 (2010), 3495-3499 Request permission
Abstract:
Using a result in the theory of tight closure on $F$-rational rings, we prove a criterion for local rings of positive prime characteristic to be complete intersections. As an application of our criterion, we give a new and simple proof for an extension of an algebraic result of Faltings that was used by Taylor and Wiles for a simplification of the proof of the minimal deformation problem.References
- David Eisenbud, Commutative algebra, Graduate Texts in Mathematics, vol. 150, Springer-Verlag, New York, 1995. With a view toward algebraic geometry. MR 1322960, DOI 10.1007/978-1-4612-5350-1
- Melvin Hochster and Craig Huneke, Tight closure, invariant theory, and the Briançon-Skoda theorem, J. Amer. Math. Soc. 3 (1990), no. 1, 31–116. MR 1017784, DOI 10.1090/S0894-0347-1990-1017784-6
- Melvin Hochster and Craig Huneke, Tight closure of parameter ideals and splitting in module-finite extensions, J. Algebraic Geom. 3 (1994), no. 4, 599–670. MR 1297848
- Craig Huneke, Tight closure and its applications, CBMS Regional Conference Series in Mathematics, vol. 88, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1996. With an appendix by Melvin Hochster. MR 1377268, DOI 10.1016/0167-4889(95)00136-0
- Hideyuki Matsumura, Commutative ring theory, 2nd ed., Cambridge Studies in Advanced Mathematics, vol. 8, Cambridge University Press, Cambridge, 1989. Translated from the Japanese by M. Reid. MR 1011461
- Kenneth A. Ribet, Galois representations and modular forms, Bull. Amer. Math. Soc. (N.S.) 32 (1995), no. 4, 375–402. MR 1322785, DOI 10.1090/S0273-0979-1995-00616-6
- Richard Taylor and Andrew Wiles, Ring-theoretic properties of certain Hecke algebras, Ann. of Math. (2) 141 (1995), no. 3, 553–572. MR 1333036, DOI 10.2307/2118560
- Andrew Wiles, Modular elliptic curves and Fermat’s last theorem, Ann. of Math. (2) 141 (1995), no. 3, 443–551. MR 1333035, DOI 10.2307/2118559
Additional Information
- Tirdad Sharif
- Affiliation: School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran
- Email: sharif@ipm.ir
- Received by editor(s): April 28, 2009
- Received by editor(s) in revised form: January 13, 2010
- Published electronically: May 10, 2010
- Additional Notes: The author was supported by a grant from IPM (No. 83130311).
- Communicated by: Bernd Ulrich
- © Copyright 2010 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 138 (2010), 3495-3499
- MSC (2010): Primary 13A35, 14M10
- DOI: https://doi.org/10.1090/S0002-9939-10-10379-7
- MathSciNet review: 2661549