Francesc Castella

collaborators

9 papers

math.NT2026

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.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.NT2026

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.NT2025

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 $F_{p} (I ¨ )$ . In this p…

math.NT2025

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.NT2025

Diagonal cycles and anticyclotomic Iwasawa theory of modular forms

Francesc Castella, Kim Tuan Do

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