Automorphic p-adic L-functions and regulators

On the construction of elements in the Iwasawa cohomology of Galois representations for GSp(2n)xGSp(2n)

15 oct. 2019, 11:00

1h

Salle de réunion (University of Lille)

Orateur

Antonio Cauchi (Université Laval)

Description

The study of arithmetic invariants associated to Galois representations has often relied on the construction of a special family of elements in their Galois cohomology groups. For instance, it has been a crucial ingredient in the work of Kato in the proof of special cases of the conjecture of Birch and Swinnerton-Dyer and the Iwasawa main conjecture for modular forms.

In this talk, we describe how to construct elements in the Iwasawa cohomology of Galois representations associated to a product of two cohomological cuspidal automorphic representations of the similitude symplectic group ${\mathrm{GSp}}_{2n}$, and, thus, p-adic L-functions using Perrin-Riou’s machinery. This construction generalises the one given by Lei-Loeffler-Zerbes when $n=1$.