Wiles defect of Hecke algebras via local-global arguments

Gebhard Boeckle, Chandrashekhar B. Khare, Jeffrey Manning

We continue our study of the Wiles defect of deformation rings $R$ and Hecke rings $T$ (at a newform $f$) acting on the cohomology of Shimura curves. The Wiles defect at an augment…