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pro vyhledávání: '"Castella, Francesc"'
Autor:
Castella, Francesc
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 of $E$ generate over $F$ an abelian extension of $K$. In this paper we
Externí odkaz:
http://arxiv.org/abs/2407.11891
We produce a flat $\Lambda$-module of $\Lambda$-adic critical slope overconvergent modular forms, producing a Hida-type theory that interpolates such forms over $p$-adically varying integer weights. This provides a Hida-theoretic explanation for an o
Externí odkaz:
http://arxiv.org/abs/2406.08460
Let $E/\mathbb{Q}$ be an elliptic curve of conductor $N$, $p$ an odd prime of good ordinary reduction such that $E[p]$ is an irreducible $G_{\mathbb{Q}}$-module, and $K$ an imaginary quadratic field with all primes dividing $Np$ split. We prove Iwasa
Externí odkaz:
http://arxiv.org/abs/2405.00270
Autor:
Castella, Francesc
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'.
Externí odkaz:
http://arxiv.org/abs/2404.12644
Let $E/\mathbb{Q}$ be an elliptic curve and $p$ an odd prime. In 1991 Kolyvagin conjectured that the system of cohomology classes for the $p$-adic Tate module of $E$ derived from Heegner points on $E$ over ring class fields of an imaginary quadratic
Externí odkaz:
http://arxiv.org/abs/2312.09301
Autor:
Castella, Francesc
A construction due to Darmon--Rotger gives rise to generalised Kato classes $\kappa_p(E)$ in the $p$-adic Selmer group ${\rm Sel}(\mathbf{Q},V_pE)$ of elliptic curves $E/\mathbf{Q}$ of positive even analytic rank, where $p>3$ is any prime of good ord
Externí odkaz:
http://arxiv.org/abs/2312.01481
Let $E/\mathbf{Q}$ 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 and in which $p$ splits. In a previous work, Agboola--Castella formulat
Externí odkaz:
http://arxiv.org/abs/2308.10474
Autor:
Castella, Francesc, Do, Kim Tuan
We construct a new anticyclotomic Euler system (in the sense of Jetchev-Nekovar-Skinner) for the Galois representation $V_{f,\chi}$ attached to a newform $f$ of weight $k\geq 2$ twisted by an anticyclotomic Hecke character $\chi$. We then show some a
Externí odkaz:
http://arxiv.org/abs/2303.06751
Let $E/\mathbb{Q}$ 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 $\mathbb{F}_p(\phi)$. In this paper we prove the cyclotomic Iwasawa main conjecture for $E$, as for
Externí odkaz:
http://arxiv.org/abs/2303.04373
Autor:
Castella, Francesc
Let $E_{/\mathbf{Q}}$ be a CM elliptic curve and $p>3$ a prime of good ordinary reduction for $E$. Assume $L(E,1)=0$ with sign $+1$ (so ${\rm ord}_{s=1}L(E,s)\geq 2$) and $E$ has a rational point of infinite order. We prove that if ${\rm Sel}(\mathbf
Externí odkaz:
http://arxiv.org/abs/2204.09608