Product formula for p-adic epsilon factors

Let X be a smooth proper curve over a finite field of characteristic p. We prove a product formula for p-adic epsilon factors of arithmetic D-modules on X. In particular we deduce the analogous formula for overconvergent F-isocrystals, which was conjectured previously. The p-adic product formula is the equivalent in rigid cohomology of the Deligne-Laumon formula for epsilon factors in l-adic \'etale cohomology (for a prime l different from p). One of the main tools in the proof of this p-adic formula is a theorem of regular stationary phase for arithmetic D-modules that we prove by microlocal techniques.Comment: Revised version: some proofs and constructions detailed, notation improved, index of notation added ; 88 page

Monitoring of water from the underground to the tree: first results with a new sap extractor on a riparian woodland

Riparian woodlands are characterized by variable hydrological conditions. Following the mapping of the complex underground water circulation of the wetlands, we studied the water uptake by trees. Although there are numerous analytical techniques available to monitor the water origin and water fluxes, no rapid technique for the extraction of xylem sap exists on the market. For this reason we designed and built a unique machine able to extract sap directly in the field from wood cores in a few minutes. A short description of the machine and its performance is given, prior to reporting the first experimental results obtained in a young riparian woodland along the Garonne River. The results compare the vertical water profile of the soil and the corresponding xylem sap at different roots horizons and in the trunk

Free-Space Graphics with Electrically Driven Levitated Light Scatterers

Levitation of optical scatterers provides a new mean to develop free-space volumetric displays. The principle is to illuminate a levitating particle displaced at high velocity in three dimensions (3D) to create images based on persistence of vision (POV). Light scattered by the particle can be observed all around the volumetric display and therefore provides a true 3D image that does not rely on interference effects and remains insensitive to the angle of observation. The challenge is to control with a high accuracy and at high speed the trajectory of the particle in three dimensions. Systems that use light to generate free-space images either in plasma or with a bead are strictly dependent of the scanning method used. Mechanical systems are required to scan the particles in the volume which weakens the time dynamics. Here we use electrically driven planar Paul traps (PPTs) to control the trajectory of electrically charged particles. A single gold particle colloid is manipulated in three dimensions through AC and DC electrical voltages applied to a PPT. Electric voltages can be modulated at high frequencies (150 kHz) and allow for a high speed displacement of particles without moving any other system component. The optical scattering of the particle in levitation yields free-space images that are imaged with conventional optics. The trajectory of the particle is entirely encoded in the electric voltage and driven through stationary planar electrodes. We show in this paper, the proof-of-concept for the generation of 3D free space graphics with a single electrically scanned particle

A Fast Algorithm for Computing the p-Curvature

We design an algorithm for computing the $p$-curvature of a differential system in positive characteristic $p$. For a system of dimension $r$ with coefficients of degree at most $d$, its complexity is \softO (p d r^\omega) operations in the ground field (where $\omega$ denotes the exponent of matrix multiplication), whereas the size of the output is about $p d r^2$. Our algorithm is then quasi-optimal assuming that matrix multiplication is (\emph{i.e.} $\omega = 2$). The main theoretical input we are using is the existence of a well-suited ring of series with divided powers for which an analogue of the Cauchy--Lipschitz Theorem holds.Comment: ISSAC 2015, Jul 2015, Bath, United Kingdo

Value-Relevance of the Outside Corporate Governance Information: a Canadian Study

This study examines whether the corporate governance rankings published by The Globe and Mail, a reputed national Canadian newspaper, are reflected in the values that investors accord to firms. A sample of 796 observations on 289 Canadian companies from 2002-2005 inclusively was analyzed using a price model (Cazavan-Jeny and JeanJean, 2006). Results suggest that the corporate governance rankings published by this market information intermediary are related not only to firm value, but also to accounting results. Thus, the relationship between corporate governance scores and market capitalization can take two forms. First, there may be a direct relationship due to investor interest in good governance practices. Second, there may be an indirect relationship due to the impact of good governance practices on the firms' accounting results. The results of this study should be useful for accounting practitioners and the various organizations involved in the regulation of corporate governance practices and the standardization of relevant data elements.Corporate governance; Financial market; Corporate governance rankings; Information intermediary; Investors; Research paper

Rational points over finite fields for regular models of algebraic varieties of Hodge type ≥1\geq 1

Let $R$ be a discrete valuation ring of mixed characteristics $(0,p)$, with finite residue field $k$ and fraction field $K$, let $k'$ be a finite extension of $k$, and let $X$ be a regular, proper and flat $R$-scheme, with generic fibre $X_K$ and special fibre $X_k$. Assume that $X_K$ is geometrically connected and of Hodge type $\geq 1$ in positive degrees. Then we show that the number of $k'$-rational points of $X$ satisfies the congruence $|X(k')| \equiv 1$ mod $|k'|$. Thanks to \cite{BBE07}, we deduce such congruences from a vanishing theorem for the Witt cohomology groups H^q(X_k, W\sO_{X_k,\Q}), for $q > 0$. In our proof of this last result, a key step is the construction of a trace morphism between the Witt cohomologies of the special fibres of two flat regular $R$-schemes $X$ and $Y$ of the same dimension, defined by a surjective projective morphism $f : Y \to X$.Comment: 85 pages. Refereed version. Signs have been modified in some definition

On the center of the ring of differential operators on a smooth variety over \bZ/p^n\bZ

We compute the center of the ring of PD differential operators on a smooth variety over \bZ/p^n\bZ confirming a conjecture of Kaledin. More generally, given an associative algebra $A_0$ over \bF_p and its flat deformation $A_n$ over \bZ/p^{n+1}\bZ we prove that under a certain non-degeneracy condition the center of $A_n$ is isomorphic to the ring of length $n+1$ Witt vectors over the center of $A_0$.Comment: 16 page

The use of the stable oxygen isotope (18O) to trace the distribution and uptake of water in riparian woodlands

Streamside vegetation forming narrow "corridors" in temperate regions, is typically dominated by deciduous tree species reflecting strong influences by human activities. Riparian woodlands depend on hydrological resources and have to adapt to rapid changes in water levels and soil moisture conditions. Three main water sources are typically present in the riparian zone: river water originating in the mountains, ground water and rainfall. Stable isotopes, such as oxygen-18, are useful tools which allow for water movement to be traced within the riparian zone and which help to identify water sources utilised by the trees growing in these areas