Finiteness theorems for the Picard objects of an algebraic stack

We prove some finiteness theorems for the Picard functor of an algebraic stack, in the spirit of SGA 6, exp. XII and XIII. In particular, we give a stacky version of Raynaud's relative representability theorem, we give sufficient conditions for the existence of the torsion component of the Picard functor, and for the finite generation of the Neron-Severi groups or of the Picard group itself. We give some examples and applications. In an appendix, we prove the semicontinuity theorem for a (non necessarily tame) algebraic stack.Comment: 29 pages. Final version, including the remarks of the referee. To appear in Adv. Mat

Proof of de Smit's conjecture: a freeness criterion

Let $A\to B$ be a morphism of Artin local rings with the same embedding dimension. We prove that any $A$-flat $B$-module is $B$-flat. This freeness criterion was conjectured by de Smit in 1997 and improves Diamond's Theorem 2.1 from his 1997 paper "The Taylor-Wiles construction and multiplicity one". We also prove that if there is a nonzero $A$-flat $B$-module, then $A\to B$ is flat and is a relative complete intersection (i.e. $B/\mathfrak{m}_AB$ is a complete intersection). Then we explain how this result allows to simplify Wiles's proof of Fermat's Last Theorem: we do not need the so-called "Taylor-Wiles systems" anymore.Comment: final version, to appear in Compositio Mathematic

Classical Political Economy Sifted Through Dialectical Reason: The Hegelian rereading

This article examines the analysis of the economic system developed by Hegel in the Elements of the Philosophy of Right. It shows how this analysis amounts not to a reworking and development of the theses of classical political economy, but rather to their dialectical reinterpretation. This particular logic of apprehension grounds the specificity of the Hegelian view of the economic sphere and its irreducibility to classical theses. The article explains how this particular logic of apprehension leads Hegel to bring to the foreground the insufficiencies of the market-based mode of coordination of individual destinies, as well as the necessity that this mode of coordination be surpassed both by and in the rational state. The article, then, focuses on the specificity of the articulation that Hegel conceives between civil society and the state. It shows how Hegel, surpassing the liberalism-state interventionism opposition, sketches an institutional device ensuring the advent of an ethical economy.Ethical economy ; civil society ; Hegel ; classical political economy

Comparison between classical potentials and ab initio for silicon under large shear

The homogeneous shear of the {111} planes along the <110> direction of bulk silicon has been investigated using ab initio techniques, to better understand the strain properties of both shuffle and glide set planes. Similar calculations have been done with three empirical potentials, Stillinger-Weber, Tersoff and EDIP, in order to find the one giving the best results under large shear strains. The generalized stacking fault energies have also been calculated with these potentials to complement this study. It turns out that the Stillinger-Weber potential better reproduces the ab initio results, for the smoothness and the amplitude of the energy variation as well as the localization of shear in the shuffle set

Decomposition driven interface evolution for layers of binary mixtures: {II}. Influence of convective transport on linear stability

We study the linear stability with respect to lateral perturbations of free surface films of polymer mixtures on solid substrates. The study focuses on the stability properties of the stratified and homogeneous steady film states studied in Part I [U. Thiele, S. Madruga and L. Frastia, Phys. Fluids 19, 122106 (2007)]. To this aim, the linearized bulk equations and boundary equations are solved using continuation techniques for several different cases of energetic bias at the surfaces, corresponding to linear and quadratic solutal Marangoni effects. For purely diffusive transport, an increase in film thickness either exponentially decreases the lateral instability or entirely stabilizes the film. Including convective transport leads to a further destabilization as compared to the purely diffusive case. In some cases the inclusion of convective transport and the related widening of the range of available film configurations (it is then able to change its surface profile) change the stability behavior qualitatively. We furthermore present results regarding the dependence of the instability on several other parameters, namely, the Reynolds number, the Surface tension number and the ratio of the typical velocities of convective and diffusive transport.Comment: Published in Physics of Fluic

Champs alg\'ebriques et foncteur de Picard

This text is my thesis, defended in June 2007, in the status it was at this time. The most important results are contained in the article "Foncteur de Picard d'un champ alg\'ebrique" to appear in "Mathematische Annalen" (see the preprint arXiv:0711.4545). In the article, some results have been added, and some previous results have been strengthened. However, the proofs of the results contained in the appendix (concerning the smooth-\'etale cohomology on an algebraic stack) have been removed. The thesis is only put on the ArXiv to provide a more lasting reference than my webpage for these proofs.Comment: Thesis, June 2007, 108 pages, to serve as a reference for another articl

Mechanical effect of absorption Carbon sequestration and swelling of coal

International audienceMechanical effect of absorption Carbon sequestration and swelling of coa