Wiles defect for Hecke algebras that are not complete intersections
Shekhar Khare - UCLA
via Zoom Video Conferencing: https://harvard.zoom.us/j/136830668
I will describe a method for precisely computing the extent to which the numerical criterion fails (i.e. the 'Wiles defect") at a newform f which gives rise to an augmentation T -> Z_p. The defect turns out to be determined entirely by local information of the newform f at the primes q dividing the discriminant of the quaternion algebra at which the mod p representation arising from f is ``trivial''. (For instance if
f corresponds to a semistable elliptic curve, then the local defect at q is related to the
``tame regulator'' of the Tate period of the elliptic curve at q.)
This is joint work with Gebhard Boeckle and Jeffrey Manning.