Seminar

The ``parity conjecture'' refers to the order of vanishing modulo 2 in the Bloch–-Kato conjecture on special values of motivic L-functions. After specializing to a class of cases where the conjecture can be formulated unconditionally, we generalize techniques of Nekov\'a\v r to show that the validity of the claim is constant in p-adic analytic families, and give applications to Hilbert modular forms. This is joint work with Liang Xiao.