J. Guàrdia

activity

20042026

most citedAbelian surfaces of GL2-type as Jacobians of curves

22 citations · 78 across the 20 of their papers we have counts for

collaborators

22 papers

math.NT2026★ 13 cited

Computations on Modular Jacobian Surfaces

Enrique González-Jiménez, Josep González, Jordi Guàrdia

We give a method for finding rational equations of genus 2 curves whose jacobians are abelian varieties $A_{f}$ attached by Shimura to normalized newforms $f \in S_{2} (Γ_{0} (N))$ . We pr…

math.AC2022★ 1 cited

Polynomial factorization over henselian fields

Maria Alberich-Carramiñana, Jordi Guàrdia, Enric Nart +3

Given a valued field $(K, v)$ and an irreducible polynomial $g \in K [x]$ , we survey the ideas of Ore, Maclane, Okutsu, Montes, Vaquié and Herrera-Olalla-Mahboub-Spivakovsky, leading…

math.AC2022

Valuations with infinite limit-depth

Maria Alberich-Carramiñana, Jordi Guàrdia, Enric Nart +1

For a certain field $K$ , we construct a valuation-algebraic valuation on the polynomial ring $K [x]$ , whose Maclane--Vaquié chain consists of an infinite (countable) number of limit…

math.NT2022

Square-free OM computation of global integral bases

Jordi Guàrdia, Enric Nart

For a prime $p$ , the OM algorithm finds the $p$ -adic factorization of an irreducible polynomial $f \in Z [x]$ in polynomial time. This may be applied to construct $p$ -integra…

math.AC2021

Okutsu frames of irreducible polynomials over henselian fields

Maria Alberich-Carramiñana, Jordi Guàrdia, Joaquím Roé +1

For a henselian valued field $(K, v)$ we establish a complete parallelism between the arithmetic properties of irreducible polynomials $F \in K [x]$ , encoded by their Okutsu frames, a…

math.AG2021

Valuative trees over valued fields

Maria Alberich-Carramiñana, Jordi Guàrdia, Enric Nart +1

For an arbitrary valued field $(K, v)$ and a given extension $v (K^{*}) ↪ Λ$ of ordered groups, we analyze the structure of the tree formed by all $Λ$ -valued extensions of…