16 citations · 21 across the 10 of their papers we have counts for
10 papers · 1 filter
Periods of modular forms and applications to the conjectures of Oda and of Prasanna-Venkatesh
Xavier Guitart, Santiago Molina
We establish several formulas relating periods of modular forms on quaternion algebras over number fields to special values of L-functions. Our main inputs are the cohomological te…
Plectic points and Hida-Rankin p-adic L-functions
Víctor Hernández, Santiago Molina
Plectic points were introduced by Fornea and Gehrmann as certain tensor products of local pointson elliptic curves over arbitrary number fields . In rank -…
Waldspurger formulas in higher cohomology
Santiago Molina
The classical Waldspurger formula, which computes periods of quaternionic automorphic forms in maximal torus, has been used in a wide variety of arithmetic applications, such as th…
Extremal p-adic L-functions
Santiago Molina Blanco
In this note we propose a new construction of cyclotomic p-adic L-functions attached to classical modular cuspidal eigenforms. This allows us to cover most known cases to date and…
An automorphic approach to Darmon points
Xavier Guitart, Marc Masdeu, Santiago Molina
We give archimedean and non-archimedean constructions of Darmon points on modular abelian varieties attached to automorphic forms over arbitrary number fields and possibly non-triv…
Eichler-Shimura isomorphism and group cohomology on arithmetic groups
Santiago Molina Blanco
The Eichler-Shimura isomorphism realizes the automorphic representation generated by an automorphic newform in certain cohomology of an arithmetic group. In this short note, we giv…
Galois action on the $\bar\mathbb{Q}$-isogeny classes of abelian surfaces with quaternionic multiplication
Santiago Molina
An abelian variety over a number field is called L-abelian variety if, for any element of the absolute Galois group of a number field L, the conjugated abelian variety is isogenous…
Equations of hyperelliptic Shimura curves
Santiago Molina
We describe an algorithm that computes explicit models of hyperelliptic Shimura curves attached to an indefnite quaternion algebra over Q and Atkin-Lehner quotients of them. It exp…
Ribet bimodules and the specialization of Heegner points
Santiago Molina
We describe the specialization of Heegner points on Shimura curves at primes of bad reduction. Moreover, we give some reciprocity laws relating the Galois action on these points to…
Parametrization of abelian -surfaces with quaternionic multiplication
Xavier Guitart, Santiago Molina
We prove that the abelian -surfaces whose endomorphism algebra is a quaternion algebra are parametrized, up to isogeny, by the -rational points of the quotient of certain Shi…