arXiv subjects

Juan-Pablo Llerena-Córdova

Publications and source records attributed to Juan-Pablo Llerena-Córdova.

3 recordsLinked to original sources

arXiv2026

On periods of Elliptic curves

Let $E$ be an elliptic curve over $\mathbb{Q}$ having split multiplicative reduction at a prime number $p$. We describe the tame part of the $\mathcal{L}$-invariant of $E$ at $p$ in terms of automorphic $p$-adic periods introduced in the work of Darmon. More precisely, we prove an equality of refined $\mathcal{L}$-invariants using twisted versions of refined exceptional zero conjectures. When the conductor of the elliptic curve is exactly $p$ and the automorphic period is attached to an optimal embedding of conductor $1$ then we prove this equality unconditionally by using the work of de-Shalit.

math.NT↗

arXiv2026

Galois subspaces for compact Riemann surfaces of genus 2

Let $X$ be a compact Riemann surface of genus 2 and $D$ a very ample divisor with $ϕ_D$ its associated embedding into $\mathbb{P}^{n}$. We consider the set $G_{X,D}$ of linear subspaces $W$ of $\mathbb{P}^n$ of codimension $2$ with projection $π_W$ such that $f_W = π_W \circ ϕ_D$ is Galois, i.e. $f_W^*k(\mathbb{P}^1) \subseteq k(X)$ is a Galois extension. It is known that $G_{X,D}$ is isomorphic to a disjoint union of projective spaces. In this article, we calculate the dimension of projective spaces in the decomposition of $G_{X,D}$, when $D$ is induced by a subgroup of $\mathrm{Aut}(X)$.

math.AG↗

arXiv2024

Numerical study of refined conjectures of the BSD type

In 1987, Mazur and Tate stated conjectures which, in some cases, resemble the classical Birch-Swinnerton-Dyer conjecture and its $p$-adic analog. We study experimentally three conjectures stated by Mazur and Tate using SageMath. Our findings indicate discrepancies in some of the original statements of some of the conjectures presented by Mazur and Tate. However, a slight modification on the statement of these conjectures does appear to hold.

math.NT↗