In paper 9, we study connections between different Euler systems by studying the Galois representations attached to critical Eisenstein series.
9. Eisenstein degeneration of Euler systems (with D. Loeffler; submitted, January 2022).
In paper 7, we obtain partial results towards the Bloch--Kato conjecture and the anticyclotomic IMC in the setting of diagonal cycles. Paper 8 is a natural continuation of that work, where we explore the setting of the symmetric square, extending results of Dasgupta and Loeffler--Zerbes to the anticyclotomic setting.
8. An anticyclotomic Euler system for adjoint modular Galois representations (with R. Alonso and F. Castella; preprint, April 2022).
7. Iwasawa theory for GL2xGL2 and diagonal cycles (with R. Alonso and F. Castella; submitted, July 2021).
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), to appear in Amer. J. Math.
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).
5. Derivatives of Beilinson--Flach classes, Gross--Stark formulas and a p-adic Harris--Venkatesh conjecture, to appear in Documenta Math.
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.
A list of my coauthors with links to their webpages:
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.