Overconvergent cohomology and quaternionic Darmon points

We develop the (co)homological tools that make effective the construction of the quaternionic Darmon points introduced by Matthew Greenberg. In addition, we use the overconvergent cohomology techniques of Pollack--Pollack to allow for the efficient calculation of such points. Finally, we provide the first numerical evidence supporting the conjectures on their rationality.Comment: Fixed some minor typos, added authors' affiliatio

Elementary matrix decomposition and the computation of Darmon points with higher conductor

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L’ensenyança de la música a l’era digital: a utilització de la pissarra digital interactiva a l’aula de música

La presència de les tecnologies de la informació i la comunicació en el món educatiu és una realitat innegable. Les polítiques educatives dels governs locals, regionals i nacionals d’arreu del món estan impulsant que els centres educatius incorporin a les seves aules recursos tecnològics que, si bé provoquen molt d’interès als mestres per les seves possibilitats com a eines d’aprenentatge, no sempre, en els processos educatius, hi garanteixen que els aprenentatges siguin de qualitat. L’article pretén reflexionar al voltant del potencial pedagògic que aporta la utilització de la pissarra digital interactiva a l’ensenyança de la música. A la fi del document, hi suggerim, als mestres especialistes de música, cinc propostes de models per utilitzar la pissarra digital interactiva, per tal de fer-ne una correcta aplicació a l’aula.Information and communications technologies have now firmly established themselves in the world of education. The educational policies of local, regional and national governments around the world are encouraging centers of education to introduce technological resources into their classrooms. Nevertheless, although many teachers are interested in these technologies for the learning possibilities that they offer, they do not always guarantee quality learning. This article reflects on the pedagogical potential of using interactive whiteboards in the teaching of music. It concludes by offering primary school teachers specializing in music teaching five methods of using the interactive whiteboard to ensure that they are correctly applied in the classroom