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

Abstract: 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.