Perrin-Riou style critical $p$-adic $L$-functions

Abstract: I will report on joint work with Denis Benois, where we gave a Perrin-Riou-style construction of Bellaïche's $p$-adic $L$-function (as well as its improvements) at a $\theta$-critical point on the eigencurve, with applications towards leading term formulae. Besides the interpolation of the Beilinson-Kato elements about this point, the key input to prove the interpolative properties is a new "eigenspace-transition via differentiation" principle.

number theory

Audience: researchers in the topic

UCLA Number Theory Seminar