A tight closure approach to a result of G. Faltings
  Using a result of M. Hochster and C. Huneke on $F$-rational rings a criterion for complete intersection rings of characteristic $p>0$ is presented. As an application, we give a completely different proof for an algebraic result of G. Faltings that was used by Taylor and Wiles in \cite{TW} for a simplification of the proof of the minimal deformation problem. 
Tirdad Sharif