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On a result of Faltings via tight closure
Author(s):
Tirdad
Sharif
Journal:
Proc. Amer. Math. Soc.
138
(2010),
3495-3499.
MSC (2010):
Primary 13A35, 14M10
Posted:
May 10, 2010
MathSciNet review:
2661549
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Abstract:
Using a result in the theory of tight closure on  -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:
-
- 1.
- D. Eisenbud, Commutative algebra with a view toward algebraic geometry, Springer, 1995. MR 1322960 (97a:13001)
- 2.
- M. Hochster, C. Huneke, Tight closure, invariant theory, and the Briançon-Skoda theorem, J. Amer. Math. Soc. 3 (1990), 31-116. MR 1017784 (91g:13010)
- 3.
- M. Hochster, C. Huneke, Tight closure of parameter ideals and splitting in module-finite extensions, J. Algebraic Geom. 3 (1994), no. 4, 599-670. MR 1297848 (95k:13002)
- 4.
- C. Huneke, Tight closure and its applications, with an appendix by Melvin Hochster. CBMS Regional Conference Series in Mathematics, 88, Amer. Math. Soc., Providence, RI, 1996. MR 1377268 (96m:13001)
- 5.
- H. Matsumura, Commutative ring theory, Cambridge Studies in Advanced Mathematics, 8, Cambridge University Press, Cambridge, 1989. MR 1011461 (90i:13001)
- 6.
- K. A. Ribet, Galois representations and modular forms, Bull. Amer. Math. Soc. (N.S.) 32 (1995), no. 4, 375-402. MR 1322785 (96b:11073)
- 7.
- R. Taylor, A. Wiles, Ring-theoretic properties of certain Hecke algebras, Ann. of Math. (2) 141 (1995), 553-572. MR 1333036 (96d:11072)
- 8.
- A. Wiles, Modular elliptic curves and Fermat's last theorem. Ann. of Math. (2) 141 (1995), no. 3, 443-551. MR 1333035 (96d:11071)
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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
DOI:
10.1090/S0002-9939-10-10379-7
PII:
S 0002-9939(10)10379-7
Keywords:
Complete intersection algebras,
deformation algebras,
Hecke algebras,
tight closure
Received by editor(s):
April 28, 2009
Received by editor(s) in revised form:
January 13, 2010
Posted:
May 10, 2010
Additional Notes:
The author was supported by a grant from IPM (No. 83130311).
Communicated by:
Bernd Ulrich
Copyright of article:
Copyright
2010,
American Mathematical Society
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