Lemmes de multiplicités et $T$-modules.

Algèbres de distributions et D-modules arithmétiques

Let p be a prime number, V a complete discrete valuation ring of unequal caracteristics (0, p), G a smooth affine algebraic group over Spec V . Using partial divided powers techniques of Berthelot, we construct arithmetic distribution algebras, with level m, generalizing the classical construction of the distribution algebra. We also construct the weak completion of the classical distribution a...

Lemmes de moyenne et Transformée aux rayons X Averaging Lemmas and the X-ray transform

We introduce a new method to prove averaging lemmas, i.e. prove a regularizing effect on the average in velocity of a solution to a kinetic equation. The method does not require the use of Fourier transform and the whole procedure is performed in the ’real space’; It leads to estimating an operator very similar to the so-called X-ray transform. We are then able to improve the known results when...

T-dual Rickart modules

We introduce the notions of T-dual Rickart and strongly T-dual Rickart modules. We provide several characterizations and investigate properties of each of these concepts. It is shown that every free (resp. finitely generated free) $R$-module is T-dual Rickart if and only if $overline{Z}^2(R)$ is a  direct summand of $R$ and End$(overline{Z}^2(R))$ is a semisimple (resp. regular) ring. It is sho...

Séparation et propriété de Deligne-Mumford des champs de modules d'intersections complètes lisses

We show that the moduli stacks of smooth complete intersections in P polarized by O(1) are separated (except for quadrics) and Deligne–Mumford (apart from a few exceptions).

Etude preliminaire de l'association de vaccins antiaphteux et antibrucellique