Automorphic p-adic L-functions and regulators

Mini-course 3: Lecture 2

15 oct. 2019, 15:30

1h

Salle de réunion (University of Lille)

Orateur

David Loeffler (University of Warwick)

Description

In the first two lectures, Loeffler will recall Hida's theory of ordinary p-adic families of modular forms, and how it was used to construct p-adic Rankin--Selberg L-functions for ${\mathrm{GL}}_2\times {\mathrm{GL}}_2$ (by Hida and Panchishkin), and triple-product L-functions for ${\mathrm{GL}}_2\times {\mathrm{GL}}_2\times {\mathrm{GL}}_2$ (by Harris--Tilouine and Darmon--Rotger).

Then he will outline the key statements of Pilloni's higher Hida theory for the symplectic group ${\mathrm{GSp}}_4$, which gives an analogous p-adic interpolation results for higher-degree coherent cohomology of Siegel threefolds, and describe how these techniques can be used to construct p-adic L-functions for ${\mathrm{GSp}}_4$, ${\mathrm{GSp}}_4\times {\mathrm{GL}}_2$, and ${\mathrm{GSp}}_4\times {\mathrm{GL}}_2\times {\mathrm{GL}}_2$, as in the recent preprint of Loeffler --Pilloni--Skinner--Zerbes.