3 papers
math.NT2025
An anticyclotomic Euler system of Hirzebruch--Zagier cycles I: Norm relations and -adic interpolation
Raúl Alonso, Francesc Castella, Óscar Rivero
We construct an anticyclotomic Euler system for the Asai Galois representation associated to -ordinary Hilbert modular forms over real quadratic fields. We also show that our Eu…
math.NT2019
The exceptional zero phenomenon for elliptic units
Óscar Rivero
The exceptional zero phenomenon has been widely studied in the realm of -adic -functions, where the starting point lies in the foundational work of Mazur, Tate and Teitelbaum…
math.NT2018
Derived Beilinson-Flach elements and the arithmetic of the adjoint of a modular form
Óscar Rivero, Victor Rotger
Kings, Lei, Loeffler and Zerbes constructed a three-variable Euler system of Beilinson-Flach elements associated to a pair of Hida families …