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Currently displaying 1 – 3 of 3

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Abelian surfaces of GL₂-type as Jacobians of curves

Josep González; Jordi Guàrdia; Victor Rotger — 2005

Acta Arithmetica

$ℒ$ -invariants and Darmon cycles attached to modular forms

Victor Rotger; Marco Adamo Seveso — 2012

Journal of the European Mathematical Society

Let $f$ be a modular eigenform of even weight $k \geq 2$ and new at a prime $p$ dividing exactly the level with respect to an indefinite quaternion algebra. The theory of Fontaine-Mazur allows to attach to $f$ a monodromy module $D_{f}^{F M}$ and an $ℒ$ -invariant $ℒ_{f}^{F M}$ . The first goal of this paper is building a suitable $p$ -adic integration theory that allows us to construct a new monodromy module $D_{f}$ and $ℒ$ -invariant $ℒ_{f}$ , in the spirit of Darmon. The two monodromy modules are isomorphic, and in particular the two $ℒ$ -invariants are equal....

The field of moduli of quaternionic multiplication on abelian varieties.

Rotger, Victor — 2004

International Journal of Mathematics and Mathematical Sciences

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