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

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

Validity and reliability of 3D marker based scapular motion analysis : a systematic review

Methods based on cutaneous markers are the most popular for the recording of three dimensional scapular motion analysis. Numerous methods have been evaluated, each showing different levels of accuracy and reliability. The aim of this review was to report the metrological properties of 3D scapular kinematic measurements using cutaneous markers and to make recommendations based on metrological evidence. A database search was conducted using relevant keywords and inclusion/exclusion criteria in 5 databases. 19 articles were included and assessed using a quality score. Concurrent validity and reliability were analyzed for each method. Six different methods are reported in the literature, each based on different marker locations and post collection computations. The acromion marker cluster (AMC) method coupled with a calibration of the scapula with the arm at rest is the most studied method. Below 90–100° of humeral elevation, this method is accurate to about 5° during arm flexion and 7° during arm abduction compared to palpation (average of the 3 scapular rotation errors). Good to excellent within-session reliability and moderate to excellent between-session reliability have been reported. The AMC method can be improved using different or multiple calibrations. Other methods using different marker locations or more markers on the scapula blade have been described but are less accurate than AMC methods. Based on current metrological evidence we would recommend (1) the use of an AMC located at the junction of the scapular spine and the acromion, (2) the use of a single calibration at rest if the task does not reach 90° of humeral elevation, (3) the use of a second calibration (at 90° or 120° of humeral elevation), or multiple calibrations above 90° of humeral elevation

Muscle activation during gait in children with Duchenne muscular dystrophy

The aim of this prospective study was to investigate changes in muscle activity during gait in children with Duchenne muscular Dystrophy (DMD). Dynamic surface electromyography recordings (EMGs) of 16 children with DMD and pathological gait were compared with those of 15 control children. The activity of the rectus femoris (RF), vastus lateralis (VL), medial hamstrings (HS), tibialis anterior (TA) and gastrocnemius soleus (GAS) muscles was recorded and analysed quantitatively and qualitatively. The overall muscle activity in the children with DMD was significantly different from that of the control group. Percentage activation amplitudes of RF, HS and TA were greater throughout the gait cycle in the children with DMD and the timing of GAS activity differed from the control children. Significantly greater muscle coactivation was found in the children with DMD. There were no significant differences between sides. Since the motor command is normal in DMD, the hyper-activity and co-contractions likely compensate for gait instability and muscle weakness, however may have negative consequences on the muscles and may increase the energy cost of gait. Simple rehabilitative strategies such as targeted physical therapies may improve stability and thus the pattern of muscle activity