## STNB2019 (33è any)

### Iwasawa theory and Euler systems: the case of diagonal cycles

#### Ponents

In this talk, we begin by motivating the use of Euler systems in the study of Iwasawa main conjectures, after Rubin, Kato and Skinner--Urban. Once we have emphasized the important role played in arithmetics by the cohomology classes arising both from Beilinson--Flach elements and diagonal cycles, we discuss different formulations of the Iwasawa main conjecture in those settings. We also explain some approaches that have been taken in the study of the Beilinson--Flach case. Finally, we report joint work in progress with Francesc Castellà concerning some instances of the conjecture for diagonal cycles, where the lack of an Euler system leads us to adopt a slightly different approach, where the interaction with $p$-adic $L$-functions plays a prominent role.