Joint IAS/PU Number Theory Seminar

In joint work with Denis Benois, we give an étale construction of Bellaïche's p-adic L-functions about θ-critical points on the Coleman–Mazur eigencurve. I will discuss applications of this construction towards leading term formulae in terms of p-adic regulators on what we call the thick Selmer groups, which come attached to the infinitesimal deformation at the said θ-critical point along the eigencurve, and a Λ-adic L-invariant. Besides our interpolation of the Beilinson–Kato elements about this point, the key input to prove the interpolative properties of this p-adic L-function is a new p-adic Hodge-theoretic "eigenspace-transition via differentiation" principle.