'Oscar Rivero

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20182025

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6 papers · 1 filter

math.NT2025

Wall-crossing and $p$ -adic Artin formalism for $GSp_{4} \times GL_{2} \times GL_{2}$

Kâzım Büyükboduk, Óscar Rivero, Ryotaro Sakamoto

The goal of this article is to develop a $p$ -adic Artin formalism in the context of $p$ -adic families of automorphic forms on $GSp_{4} \times GL_{2} \times GL_{2}$ . Our…

math.NT2025

Anticyclotomic diagonal classes and Beilinson--Flach elements

Raúl Alonso, Lois Omil-Pazos, Óscar Rivero

We present a comparison between the anticyclotomic Euler system of diagonal cycles associated with the convolution of two modular forms and the cyclotomic Beilinson--Flach Euler sy…

math.NT2025

An anticyclotomic Euler system of Hirzebruch--Zagier cycles I: Norm relations and $p$ -adic interpolation

Raúl Alonso, Francesc Castella, Óscar Rivero

We construct an anticyclotomic Euler system for the Asai Galois representation associated to $p$ -ordinary Hilbert modular forms over real quadratic fields. We also show that our Eu…

math.NT2025

Eisenstein degeneration of Beilinson--Kato classes and circular units

Javier Polo, Óscar Rivero, Ju-Feng Wu

The aim of this note is to explore the Euler system of Beilinson--Kato elements in families passing through the critical $p$ -stabilization of an Eisenstein series attached to two D…

math.NT2019

The exceptional zero phenomenon for elliptic units

Óscar Rivero

The exceptional zero phenomenon has been widely studied in the realm of $p$ -adic $L$ -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 $κ (g, h)$ of Beilinson-Flach elements associated to a pair of Hida families $(g, h)$ …

Wall-crossing and p-adic Artin formalism for GSp4​×GL2​×GL2​

Anticyclotomic diagonal classes and Beilinson--Flach elements

An anticyclotomic Euler system of Hirzebruch--Zagier cycles I: Norm relations and p-adic interpolation

Eisenstein degeneration of Beilinson--Kato classes and circular units

The exceptional zero phenomenon for elliptic units

Derived Beilinson-Flach elements and the arithmetic of the adjoint of a modular form

Wall-crossing and $p$ -adic Artin formalism for $GSp_{4} \times GL_{2} \times GL_{2}$

An anticyclotomic Euler system of Hirzebruch--Zagier cycles I: Norm relations and $p$ -adic interpolation