# Automorphic p-adic L-functions and regulators

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

## An explicit reciprocity law for the GSp(4)-Euler system

18 Oct 2019, 09:30
1h
Salle de réunion (University of Lille)

### Salle de réunion

#### University of Lille

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

### Speaker

Sarah Zerbes (University College London)

### Description

I will report on work in progress with David Loeffler and Chris Skinner. I will sketch a proof for of an explicit reciprocity law for the Euler system attached to the spin representation of genus $2$ Siegel modular forms, relating the Euler system to the spin $p$-adic $L$-function that we constructed in joint work with Vincent Pilloni. As an application, we obtain bounds on Selmer groups, conditional on the nonvanishing of non-critical $p$-adic $L$-values.

### Presentation Materials

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