Xavier Guitart

activity

20092025

most citedDarmon points on elliptic curves over number fields of arbitrary signature

18 citations · 60 across the 23 of their papers we have counts for

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3 papers · 1 filter

math.NT2009

Parametrization of abelian $K$ -surfaces with quaternionic multiplication

Xavier Guitart, Santiago Molina

We prove that the abelian $K$ -surfaces whose endomorphism algebra is a quaternion algebra are parametrized, up to isogeny, by the $K$ -rational points of the quotient of certain Shi…

math.NT2009

Fields of definition of building blocks with quaternionic multiplication

Xavier Guitart

This paper investigates the fields of definition up to isogeny of the abelian varieties called building blocks. A result of Ribet characterizes the fields of definition of these va…

math.NT2009★ 11 cited

Modular abelian varieties over number fields

Xavier Guitart, Jordi Quer

The main result of this paper is a characterization of the abelian varieties $B / K$ defined over Galois number fields with the property that the zeta function $L (B / K; s)$ is equivale…

Parametrization of abelian K-surfaces with quaternionic multiplication

Fields of definition of building blocks with quaternionic multiplication

Modular abelian varieties over number fields

Parametrization of abelian $K$ -surfaces with quaternionic multiplication