1. CJM 2013 (vol 66 pp. 1167)
 Rotger, Victor; de VeraPiquero, Carlos

Galois Representations Over Fields of Moduli and Rational Points on Shimura Curves
The purpose of this note is introducing a method for proving the
existence of no rational points on a coarse moduli space $X$ of abelian varieties
over a given number field $K$, in cases where the moduli problem is not fine and
points in $X(K)$ may not be represented by an abelian variety (with additional structure)
admitting a model over the field $K$. This is typically the case when the abelian
varieties that are being classified have even dimension. The main idea, inspired on
the work of Ellenberg and Skinner on the modularity of $\mathbb{Q}$curves, is that to a
point $P=[A]\in X(K)$ represented by an abelian variety $A/\bar K$ one may still
attach a Galois representation of $\operatorname{Gal}(\bar K/K)$ with values in the quotient
group $\operatorname{GL}(T_\ell(A))/\operatorname{Aut}(A)$, provided
$\operatorname{Aut}(A)$ lies in the centre of $\operatorname{GL}(T_\ell(A))$.
We exemplify our method in the cases where $X$ is a Shimura curve over an imaginary
quadratic field or an AtkinLehner quotient over $\mathbb{Q}$.
Keywords:Shimura curves, rational points, Galois representations, Hasse principle, BrauerManin obstruction Categories:11G18, 14G35, 14G05 

2. CJM 2011 (vol 64 pp. 1122)
 Seveso, Marco Adamo

$p$adic $L$functions and the Rationality of Darmon Cycles
Darmon cycles are a higher weight analogue of StarkHeegner points. They
yield local cohomology classes in the Deligne representation associated with a
cuspidal form on $\Gamma _{0}( N) $ of even weight $k_{0}\geq 2$.
They are conjectured to be the restriction of global cohomology classes in
the BlochKato Selmer group defined over narrow ring class fields attached
to a real quadratic field. We show that suitable linear combinations of them
obtained by genus characters satisfy these conjectures. We also prove $p$adic GrossZagier type formulas, relating the derivatives of $p$adic $L$functions of the weight variable attached to imaginary (resp. real)
quadratic fields to Heegner cycles (resp. Darmon cycles). Finally we express
the second derivative of the MazurKitagawa $p$adic $L$function of the
weight variable in terms of a global cycle defined over a quadratic
extension of $\mathbb{Q}$.
Categories:11F67, 14G05 
