Resumen de On a result of Faltings via tight closure

Tirdad Sharif

• 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.