Complete addition laws on abelian varieties

We prove that under any projective embedding of an abelian variety A of dimension g, a complete system of addition laws has cardinality at least g+1, generalizing of a result of Bosma and Lenstra for the Weierstrass model of an elliptic curve in P^2. In contrast with this geometric constraint, we moreover prove that if k is any field with infinite absolute Galois group, then there exists, for every abelian variety A/k, a projective embedding and an addition law defined for every pair of k-rational points. For an abelian variety of dimension 1 or 2, we show that this embedding can be the classical Weierstrass model or embedding in P^15, respectively, up to a finite number of counterexamples for |k| less or equal to 5.Comment: 9 pages. Finale version, accepted for publication in LMS Journal of Computation and Mathematic

The Two Dimensional Euler Equations on Singular Exterior Domains

This paper is a follow-up of article [Gerard-Varet and Lacave, ARMA 2013], on the existence of global weak solutions to the two dimensional Euler equations in singular domains. In [Gerard-Varet and Lacave, ARMA 2013], we have established the existence of weak solutions for a large class of bounded domains, with initial vorticity in $L^p$ ($p>1$). For unbounded domains, we have proved a similar result only when the initial vorticity is in $L^p_{c}$ ($p>2$) and when the domain is the exterior of a single obstacle. The goal here is to retrieve these two restrictions: we consider general initial vorticity in $L^1\cap L^p$ ($p>1$), outside an arbitrary number of obstacles (not reduced to points)

Towards an Updatable Strategy Logic

This article is about temporal multi-agent logics. Several of these formalisms have been already presented (ATL-ATL*, ATLsc, SL). They enable to express the capacities of agents in a system to ensure the satisfaction of temporal properties. Particularly, SL and ATLsc enable several agents to interact in a context mixing the different strategies they play in a semantical game. We generalize this possibility by proposing a new formalism, Updating Strategy Logic (USL). In USL, an agent can also refine its own strategy. The gain in expressive power rises the notion of "sustainable capacities" for agents. USL is built from SL. It mainly brings to SL the two following modifications: semantically, the successor of a given state is not uniquely determined by the data of one choice from each agent. Syntactically, we introduce in the language an operator, called an "unbinder", which explicitely deletes the binding of a strategy to an agent. We show that USL is strictly more expressive than SL.Comment: In Proceedings SR 2013, arXiv:1303.007

The Weierstrass subgroup of a curve has maximal rank

We show that the Weierstrass points of the generic curve of genus $g$ over an algebraically closed field of characteristic 0 generate a group of maximal rank in the Jacobian

Homology of origamis with symmetries

Given an origami (square-tiled surface) M with automorphism group G, we compute the decomposition of the first homology group of M into isotypic G-submodules. Through the action of the affine group of M on the homology group, we deduce some consequences for the multiplicities of the Lyapunov exponents of the Kontsevich-Zorich cocycle. We also construct and study several families of interesting origamis illustrating our results.Comment: 36 pages, no figures. Final version incorporating the referee's comments. To appear in Annales de l'Institut Fourier, Volume 64 (2014

Associating wheat crop and undersown forage legumes in organic agriculture: Incidence of forage legumes species

One of the key issues of organic arable systems is to increase use of N2 fixation from legume plants while enhancing autonomy by the limitation of off-farm inputs. Wheat yield in organic agriculture is generally low and variable. Grain yield and protein content are strongly affected by N deficiency and weed competition (Casagrande et al., 2009). Previous research had clearly demonstrated the benefits of forage legumes to improve N balance and preserve weed infestation (den Hollander et al., 2007). Several authors highlighted the interest of crop mixtures combining cereal and legumes to provide higher overall productivity, enhance ecological services and improve economical profitability (Malezieux et al., 2008). Nevertheless, previous research also highlights how important it is to manage whether above- and belowground interactions between species to optimise benefits and limit competition. We propose here to analyse how the insertion of legumes species influences the performance of organic wheat (yield, grain protein content) but also the weeds population during and after crop cycle

Incidence of soil N fertility on the performance of organic forage legume-wheat mixtures.

One of the key issues of organic arable systems is to bring enough nitrogen in the crop rotation to ensure satisfying crop nutrition. Wheat yield in organic agriculture are generally low and variable. Grain yield and grain protein content are strongly affected by N deficiency and weed competition (Casagrande et al., 2009). Nevertheless, the autonomy of the organic cropping systems has to be improved while off-farm inputs have to be limited. The use of N2 fixation from legume plants should then be improved. Previous research had clearly demonstrated the benefits of forage legumes in association to improve N balance and control weed seed bank. However, it is also well known that legume N2 fixation could be limited depending on the soil N fertility. The functioning of such mixtures could then be disturbed by variations of the nitrogen fertility of the environment. The impact of soil N fertility has to be studied in order to manage whether above- and belowground interactions between species and to optimise benefits of the association