Séminaire TNGA : Ting-Han Huang

Orateur : Ting-Han Huang (LAGA, Université Paris XIII)

Titre : On the pull-back method for p-adic regulator formulae

Résumé : Constructing a p-adic L-function and proving the associated regulator formula have been a powerful tool for the Bloch–Kato conjecture. In the past few decades, proofs of the regulator formulae for various p-adic L-functions mostly belong to the so-called ‘push-forward’ situation, and use syntomic/finite polynomial cohomology for computation.

Recently, Marco Sangiovanni Vincentelli and Christopher Skinner constructed an Euler system for the adjoint of a modular form via the ‘pull-back’ method, which does not use the language of finite polynomial cohomology.

Inspired by their work, A. Kazi, L. Marannino, and the speaker reconstructed the diagonal class for the
triple product via pull-back. Moreover, we proved the regulator formula for the p-adic Asai L-function for
finite slope families.

This talk will mainly focus on the first part and proceed in a survey-manner.