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On a result of Faltings via tight closure

Author: Tirdad Sharif
Journal: Proc. Amer. Math. Soc. 138 (2010), 3495-3499
MSC (2010): Primary 13A35, 14M10
Published electronically: May 10, 2010
MathSciNet review: 2661549
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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.

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Tirdad Sharif
Affiliation: School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran

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
Published electronically: May 10, 2010
Additional Notes: The author was supported by a grant from IPM (No. 83130311).
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2010 American Mathematical Society

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