Jacques Tilouine (Univ. Paris Nord)
Integral period relations and the Bloch-Kato Conjecture
for the quadratic twists of the adjoint motive of a classical modular form
It follows from works by Hida and Wiles that under certain conditions
-including minimality and residual irreducibility,
the Bloch-Kato conjecture holds for the adjoint motive of an elliptic cusp form.
In a joint work with E. Urban, we prove under
similar assumptions that it also holds
for any (real or imaginary) quadratic twist of the adjoint motive
of an elliptic cusp form.