14-18 October 2019
University of Lille
Europe/Paris timezone

Mini-course 3: Lecture 1

14 Oct 2019, 15:30
Salle de réunion (University of Lille)

Salle de réunion

University of Lille

Cité Scientifique – Bâtiment M2 59655 Villeneuve d'Ascq Cedex France


David Loeffler (University of Warwick)


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.

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