We study the variation of
-invariants
of modular forms in a cuspidal Hida family in the case that the family intersects an Eisenstein
family. We allow for intersections that occur because of “trivial zeros” (that is, because
divides an
Euler factor) as in Mazur’s Eisenstein ideal paper, and pay special attention to the case of the
-adic family passing
through the elliptic curve
.
In memory of Joël Bellaïche
Keywords
Iwasawa theory, congruences of modular forms, Iwasawa
invariants, Eisenstein congruences
