Seminar

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I will report on joint work with Denis Benois, where we give an étale construction of Bellaïche's $p$-adic L-functions about $\theta$-critical points on the eigencurve (where it ramifies over the weight space). I will review applications of this construction towards leading term formulae that involve $p$-adic regulators on "thick Selmer groups" (which come attached to the infinitesimal deformation along the eigencurve), and a $\Lambda$-adic $\mathcal{L}$-invariant. Besides our interpolation of the Beilinson--Kato elements about the $\theta$-critical point, the key input is a new $p$-adic Hodge-theoretic "eigenspace transition via differentiation" principle. 

I will concentrate on aspects that weren't covered in Denis' talk at the opening workshop, or my talks in other meetings.

ES Program Research Seminar: Arithmetic Of Critical P-Adic L-Functions