Francesc Castella

activity

20142026

most citedA proof of Perrin-Riou's Heegner point main conjecture

28 citations · 105 across the 29 of their papers we have counts for

collaborators

34 papers

math.NT2026

Kato's main conjecture for nonordinary modular forms

Francesc Castella, Zheng Liu, Xin Wan

We prove Kato's main conjecture for modular forms at nonordinary primes for weights in the Fontaine-Laffaille range. The key ingredients in the proof are a reformulation of the con…

math.NT2026

On refined nonvanishing conjectures by Kurihara and Kolyvagin

Francesc Castella, Takamichi Sano

In this paper, we extend the results of \cite{BCGS} on refined conjectures by Kurihara and Kolyvagin, allowing primes of any reduction type in the case of Kurihara's conjectures, a…

math.NT2025

A formula of Perrin-Riou and characteristic power series of signed Selmer groups

Francesc Castella

We prove a conjecture of Kundu--Ray, following from the $p$ -adic Birch--Swinnerton-Dyer conjecture for supersingular primes by Bernardi--Perrin-Riou and Kato's Main Conjecture, pre…

math.NT2024

Exceptional zeros for Heegner points and $p$ -converse to the theorem of Gross-Zagier and Kolyvagin

Francesc Castella

We prove a $p$ -converse to the theorem of Gross-Zagier and Kolyvagin for elliptic curves $E / Q$ at primes $p > 3$ of multiplicative reduction. Two key ingredients in the argu…

math.NT2024

Tamagawa number conjecture for CM modular forms and Rankin--Selberg convolutions

Francesc Castella

Let $E / F$ be an elliptic curve defined over a number field $F$ with complex multiplication by the ring of integers of an imaginary quadratic field $K$ such that the torsion points…

math.NT2024

Base change and Iwasawa Main Conjectures for $GL_{2}$

Ashay Burungale, Francesc Castella, Christopher Skinner

Let $E$ be an elliptic curve defined over $Q$ of conductor $N$ , $p$ an odd prime of good ordinary reduction such that $E [p]$ is an irreducible Galois module, and $K$ an im…

math.NT2024★ 1 cited

On the Iwasawa theory of elliptic curves at Eisenstein primes

Francesc Castella

These are expanded notes for the mini-course given by the author at the 2022 ICTS workshop `Elliptic curves and the special values of $L$ -functions'.

math.NT2023

Nonvanishing of generalised Kato classes and Iwasawa main conjectures

Francesc Castella

A construction due to Darmon--Rotger gives rise to generalised Kato classes $κ_{p} (E)$ in the $p$ -adic Selmer group $Sel (Q, V_{p} E)$ of elliptic curves $E / Q$ of…

math.NT2023★ 1 cited

Non-vanishing of Kolyvagin systems and Iwasawa theory

Ashay Burungale, Francesc Castella, Giada Grossi +1

Let $E / Q$ be an elliptic curve and $p$ an odd prime. In 1991 Kolyvagin conjectured that the system of cohomology classes for torsion quotients of the $p$ -adic Tate module…

math.NT2023

Derived $p$ -adic heights and the leading coefficient of the Bertolini--Darmon--Prasanna $p$ -adic $L$ -function

Francesc Castella, Chi-Yun Hsu, Debanjana Kundu +2

Let $E / Q$ be an elliptic curve and let $p$ be an odd prime of good reduction for $E$ . Let $K$ be an imaginary quadratic field satisfying the classical Heegner hypothesis a…

math.NT2023

Diagonal cycles and anticyclotomic Iwasawa theory of modular forms

Francesc Castella, Kim Tuan Do

We construct a new Euler system for the Galois representation $V_{f, χ}$ attached to a newform $f$ of weight $2 r \geq 2$ twisted by an anticyclotomic Hecke character $χ$ . The Euler s…

math.NT2023★ 3 cited

Mazur's main conjecture at Eisenstein primes

Francesc Castella, Giada Grossi, Christopher Skinner

Let $E / Q$ be an elliptic curve, let $p > 2$ be a prime of good reduction for $E$ , and assume that $E$ admits a rational $p$ -isogeny with kernel $F_{p} (ϕ)$ . In this pa…

math.NT2022

Generalised Kato classes on CM elliptic curves of rank 2

Francesc Castella

Let $E / Q$ be a CM elliptic curve and let $p \geq 5$ be a prime of good ordinary reduction for $E$ . Suppose that $L (E, s)$ vanishes at $s = 1$ and has sign $+ 1$ in its function…

math.NT2022★ 1 cited

An anticyclotomic Euler system for adjoint modular Galois representations

Raúl Alonso, Francesc Castella, Óscar Rivero

Let $K$ be an imaginary quadratic field and $p$ a prime split in $K$ . In this paper we construct an anticyclotomic Euler system for the adjoint representation attached to elliptic…

math.NT2021★ 1 cited

Iwasawa-Greenberg main conjecture for non-ordinary modular forms and Eisenstein congruences on $GU (3, 1)$

Francesc Castella, Zheng Liu, Xin Wan

In this paper we prove one side divisibility of the Iwasawa-Greenberg main conjecture for Rankin-Selberg product of a weight two cusp form and an ordinary CM form of higher weight,…

math.NT2021

The diagonal cycle Euler system for $GL_{2} \times GL_{2}$

Raúl Alonso, Francesc Castella, Óscar Rivero

We construct an anticyclotomic Euler system for the Rankin-Selberg convolution of two modular forms, using $p$ -adic families of generalized Gross-Kudla-Schoen diagonal cycles. As a…

math.NT2020★ 17 cited

On the anticyclotomic Iwasawa theory of rational elliptic curves at Eisenstein primes

Francesc Castella, Giada Grossi, Jaehoon Lee +1

Let $E / Q$ be an elliptic curve, and $p$ a prime where $E$ has good reduction, and assume that $E$ admits a rational $p$ -isogeny. In this paper, we study the anticyclotomic…

math.NT2020★ 1 cited

The Iwasawa Main Conjectures for $GL_{2}$ and derivatives of $p$ -adic $L$ -functions

Francesc Castella, Xin Wan

We prove under mild hypotheses the three-variable Iwasawa main conjecture for $p$ -ordinary modular forms in the indefinite setting. Our result is in a setting complementary to that…

math.NT2019

On anticyclotomic variants of the $p$ -adic Birch and Swinnerton-Dyer conjecture

Adebisi Agboola, Francesc Castella

We formulate analogues of the Birch and Swinnerton-Dyer conjecture for the $p$ -adic $L$ -functions of Bertolini-Darmon-Prasanna attached to elliptic curves $E / Q$ at primes…

math.NT2019★ 28 cited

A proof of Perrin-Riou's Heegner point main conjecture

Ashay Burungale, Francesc Castella, Chan-Ho Kim

Let $E / Q$ be an elliptic curve of conductor $N$ , let $p > 3$ be a prime where $E$ has good ordinary reduction, and let $K$ be an imaginary quadratic field satisfying the Hee…

math.NT2018★ 1 cited

On the non-vanishing of generalized Kato classes for elliptic curves of rank $2$

Francesc Castella, Ming-Lun Hsieh

We prove the first cases of a conjecture by Darmon--Rotger on the non-vanishing of generalized Kato classes attached to elliptic curves $E$ over $Q$ of rank $2$ . Our metho…

math.NT2018★ 6 cited

Class groups and local indecomposability for non-CM forms

Francesc Castella, Carl Wang-Erickson, Haruzo Hida

In the late 1990's, R. Coleman and R. Greenberg (independently) asked for a global property characterizing those $p$ -ordinary cuspidal eigenforms whose associated Galois representa…

math.NT2018★ 1 cited

Indivisibility of Heegner points and arithmetic applications

Ashay Burungale, Francesc Castella, Chan-Ho Kim

We upgrade Howard's divisibility towards Perrin-Riou's Heegner point main conjecture to the predicted equality. Contrary to previous works in this direction, our main result allows…

math.NT2018★ 11 cited

On the Iwasawa main conjectures for modular forms at non-ordinary primes

Francesc Castella, Mirela Çiperiani, Christopher Skinner +1

In this paper, we prove under mild hypotheses the Iwasawa main conjectures of Lei--Loeffler--Zerbes for modular forms of weight $2$ at non-ordinary primes. Our proof is based on th…

Kato's main conjecture for nonordinary modular forms

On refined nonvanishing conjectures by Kurihara and Kolyvagin

A formula of Perrin-Riou and characteristic power series of signed Selmer groups

Exceptional zeros for Heegner points and p-converse to the theorem of Gross-Zagier and Kolyvagin

Tamagawa number conjecture for CM modular forms and Rankin--Selberg convolutions

Base change and Iwasawa Main Conjectures for GL2​

On the Iwasawa theory of elliptic curves at Eisenstein primes

Nonvanishing of generalised Kato classes and Iwasawa main conjectures

Non-vanishing of Kolyvagin systems and Iwasawa theory

Derived p-adic heights and the leading coefficient of the Bertolini--Darmon--Prasanna p-adic L-function

Diagonal cycles and anticyclotomic Iwasawa theory of modular forms

Mazur's main conjecture at Eisenstein primes

Generalised Kato classes on CM elliptic curves of rank 2

An anticyclotomic Euler system for adjoint modular Galois representations

Iwasawa-Greenberg main conjecture for non-ordinary modular forms and Eisenstein congruences on GU(3,1)

The diagonal cycle Euler system for GL2​×GL2​

On the anticyclotomic Iwasawa theory of rational elliptic curves at Eisenstein primes

The Iwasawa Main Conjectures for GL2​ and derivatives of p-adic L-functions

On anticyclotomic variants of the p-adic Birch and Swinnerton-Dyer conjecture

A proof of Perrin-Riou's Heegner point main conjecture

On the non-vanishing of generalized Kato classes for elliptic curves of rank 2

Class groups and local indecomposability for non-CM forms

Indivisibility of Heegner points and arithmetic applications

On the Iwasawa main conjectures for modular forms at non-ordinary primes

Exceptional zeros for Heegner points and $p$ -converse to the theorem of Gross-Zagier and Kolyvagin

Base change and Iwasawa Main Conjectures for $GL_{2}$

Derived $p$ -adic heights and the leading coefficient of the Bertolini--Darmon--Prasanna $p$ -adic $L$ -function

Iwasawa-Greenberg main conjecture for non-ordinary modular forms and Eisenstein congruences on $GU (3, 1)$

The diagonal cycle Euler system for $GL_{2} \times GL_{2}$

The Iwasawa Main Conjectures for $GL_{2}$ and derivatives of $p$ -adic $L$ -functions

On anticyclotomic variants of the $p$ -adic Birch and Swinnerton-Dyer conjecture

On the non-vanishing of generalized Kato classes for elliptic curves of rank $2$