In paper 7, we obtain partial results towards the Bloch--Kato conjecture and the anticyclotomic IMC in the setting of diagonal cycles.
7. Iwasawa theory for GL2xGL2 and diagonal cycles (with R. Alonso and F. Castella; preprint).
Paper 6 is the first work in our investigations of an Artin formalism for Euler systems. In forthcoming work, we expect to explore this phenomenon in the setting of other Euler systems of Rankin--Selberg type.
6. Motivic congruences and Sharifi's conjecture (with V. Rotger, submitted, January 2021).
These 5 papers study the interplay between Beilinson--Flach classes, Hida--Rankin p-adic L-functions and Gross--Stark units, with an emphasis on the exceptional zero situation. More precisely, papers 1, 3 and 5 can be read as a trilogy. Articles 2 and 4 look at rather related instances of this philosophy, where interesting phenomena arise (the third article focuses on the case of elliptic units, while the fourth article deals with the setting of diagonal cycles). Together with paper 6 above, they constitute my doctoral thesis.
5. Cyclotomic derivatives of Beilinson--Flach classes and a new proof of a Gross--Stark formula (submitted, February 2021).
3. Derived Beilinson--Flach elements and the arithmetic of the adjoint of a modular form (with V. Rotger), J. Eur. Math. Soc. 23 (2021), no. 7, 2299--2335.
2. The exceptional zero phenomenon for elliptic units, Rev. Mat. Iberoam. 37 (2021), no. 4, 1333--1364.
1. Beilinson--Flach elements, Stark units, and p-adic iterated integrals (with V. Rotger), Forum Math. 31 (2019), no. 6, 1517--1532.
My PhD thesis (February 2021), Arithmetic applications of the Euler systems of Beilinson--Flach elements and diagonal cycles, done under the supervision of Victor Rotger.