Computing automorphic forms on Shimura curves over fields with arbitrary class number

We extend methods of Greenberg and the author to compute in the cohomology of a Shimura curve defined over a totally real field with arbitrary class number. Via the Jacquet-Langlands correspondence, we thereby compute systems of Hecke eigenvalues associated to Hilbert modular forms of arbitrary level over a totally real field of odd degree. We conclude with two examples which illustrate the effectiveness of our algorithms.Comment: 15 pages; final submission to ANTS I

On the existence of abelian surfaces with everywhere good reduction

Let $D \le 2000$ be a positive discriminant such that $F = \mathbf{Q}(\sqrt{D})$ has narrow class one, and $A/F$ an abelian surface of ${\rm GL}_2$-type with everywhere good reduction. Assuming that $A$ is modular, we show that $A$ is either an $F$-surface or is a base change from $\mathbf{Q}$ of an abelian surface $B$ such that ${\rm End}_{\mathbf{Q}}(B) = \mathbf{Z}$, except for $D = 353, 421, 1321, 1597$ and $1997$. In the latter case, we show that there are indeed abelian surfaces with everywhere good reduction over $F$ for $D = 353, 421$ and $1597$, which are non-isogenous to their Galois conjugates. These are the first known such examples

An intriguing hyperelliptic Shimura curve quotient of genus 16

Let $F$ be the maximal totally real subfield of $\mathbf{Q}(\zeta_{32})$, the cyclotomic field of $32$nd roots of unity. Let $D$ be the quaternion algebra over $F$ ramified exactly at the unique prime above $2$ and 7 of the real places of $F$. Let $\mathcal{O}$ be a maximal order in $D$, and $X_0^D(1)$ the Shimura curve attached to $\mathcal{O}$. Let $C = X_0^D(1)/\langle w_D \rangle$, where $w_D$ is the unique Atkin-Lehner involution on $X_0^D(1)$. We show that the curve $C$ has several striking features. First, it is a hyperelliptic curve of genus $16$, whose hyperelliptic involution is exceptional. Second, there are $34$ Weierstrass points on $C$, and exactly half of these points are CM points; they are defined over the Hilbert class field of the unique CM extension $E/F$ of class number $17$ contained in $\mathbf{Q}(\zeta_{64})$, the cyclotomic field of $64$th roots of unity. Third, the normal closure of the field of $2$-torsion of the Jacobian of $C$ is the Harbater field $N$, the unique Galois number field $N/\mathbf{Q}$ unramified outside $2$ and $\infty$, with Galois group $\mathrm{Gal}(N/\mathbf{Q})\simeq F_{17} = \mathbf{Z}/17\mathbf{Z} \rtimes (\mathbf{Z}/17\mathbf{Z})^\times$. In fact, the Jacobian $\mathrm{Jac}(X_0^D(1))$ has the remarkable property that each of its simple factors has a $2$-torsion field whose normal closure is the field $N$. Finally, and perhaps the most striking fact about $C$ is that it is also hyperelliptic over $\mathbf{Q}$

A three DOF linear ultrasonic motor for transport and micropositionning.

International audienceThe paper deals with the study and use of a linear ultrasonic motor at low voltages. Standing waves are generated in a 64 x 38 x 2.5 mm3 vibrator by 20 piezoelectric ceramics and converted into sliding motions by the friction between four legs and the worktop : translations and rotations are achieved. The speed of the motor is studied according to the amplitude and frequency of the driving voltage as well as the mass of the load. Then, a model of the system is retrieved for some set points and validated using a position control. According to its interesting performances for transport and positioning, the motor is used to motorize a moving palet for the transfer of parts in a microassembly workcell

Contribution du SIG à la Prévention et à la Gestion des Risques d’inondation dans le District de Bamako au Mali

En raison de sa situation géographique, la ville de Bamako reste fortement vulnérable aux risques d’inondations. La présente étude a pour objectif de mettre en exergue un outil opérationnel et évolutif d’aide à la prise de décisions en matière de prévention et de gestion des risques d’inondations dans le District de Bamako en République du Mali. Il s’agit d’élaborer à partir du Système d’Information Géographique des grilles d’analyse et d’évaluation permettant aux décideurs de mieux appréhender les risques naturels. La méthodologie adoptée s’est appuyée sur une approche par télédétection appuyée par des enquêtes et relevés de terrain. Les résultats de l’étude ont montré que les nombreux aménagements réalisés à travers la ville grâce aux politiques publiques urbaines, ont entrainé d’importants changements spatiaux-temporels. Toutefois, des occupations anarchiques règnent toujours dans la ville de Bamako, notamment sur les berges des cours d’eau qui constituent à priori des zones inondables. Des constructions existent dans les zones à risque où la vulnérabilité des populations reste forte. Les cartes réalisées indiquent les zones à stress et orientent les décideurs dans les options d’aménagement pour une réduction des risques d’inondation dans les années à venir au travers de la planification urbaine et de la participation des populations touchées dans l’élaboration des stratégies d’adaptation. Due to its geographical location, the city of Bamako remains highly vulnerable to flood risk. The objective of this study is to highlight an operational and evolving decision support tool for flood risk prevention and management in the Bamako District of the Republic ofMali. This is to develop from the Geographic Information System grids analysis and evaluation for decision-makers to better understand natural risks. The methodology adopted was based on an exploratory approach sustained by field surveys and the analysis of cartographic data. The results of the study showed that the numerous developments carried out throughout the city by urban public policies have led to a great spatial "metamorphosis". However, anarchic occupations are still a reality in the city of Bamako, especially on the banks of rivers are a priori vulnerable areas. Buildings exist in risk areas where people's vulnerability remains high. The maps produced indicate areas of stress and guide decision makers in management options for flood risk reduction in the coming years through urban planning and the participation of affected populations in the development of adaptation strategies