Serre Theorem for involutory Hopf algebras

We call a monoidal category ${\mathcal C}$ a Serre category if for any $C$, $D \in {\mathcal C}$ such that C\ot D is semisimple, $C$ and $D$ are semisimple objects in ${\mathcal C}$. Let $H$ be an involutory Hopf algebra, $M$, $N$ two $H$-(co)modules such that $M \otimes N$ is (co)semisimple as a $H$-(co)module. If $N$ (resp. $M$) is a finitely generated projective $k$-module with invertible Hattory-Stallings rank in $k$ then $M$ (resp. $N$) is (co)semisimple as a $H$-(co)module. In particular, the full subcategory of all finite dimensional modules, comodules or Yetter-Drinfel'd modules over $H$ the dimension of which is invertible in $k$ are Serre categories.Comment: a new version: 8 page

Realisation of the D067 project: implementation of the CPS accelerator complex control system

The aim of this document is to give a general overview of the implementation of the CPS Accelerator Complex Control System as a part of the D067 project. Within the framework of this project, the main reasons for the collaboration between PS and SL Divisions, which allowed the common design of the accelerator control system, will be reiterated. A description of the basic concepts and constraints, m ain parts, operator interface and applications, exploitation and future evolution of the CPS realisation of this common accelerator control system is given. A chronological list of references (main ly of conference presentations) completes the report

Some genus 3 curves with many points

Using an explicit family of plane quartic curves, we prove the existence of a genus 3 curve over any finite field of characteristic 3 whose number of rational points stays within a fixed distance from the Hasse-Weil-Serre upper bound. We also provide an intrinsic characterization of so-called Legendre elliptic curves

Serre's "formule de masse" in prime degree

For a local field F with finite residue field of characteristic p, we describe completely the structure of the filtered F_p[G]-module K^*/K^*p in characteristic 0 and $K^+/\wp(K^+) in characteristic p, where K=F(\root{p-1}\of F^*) and G=\Gal(K|F). As an application, we give an elementary proof of Serre's mass formula in degree p. We also determine the compositum C of all degree p separable extensions with solvable galoisian closure over an arbitrary base field, and show that C is K(\root p\of K^*) or K(\wp^{-1}(K)) respectively, in the case of the local field F. Our method allows us to compute the contribution of each character G\to\F_p^* to the degree p mass formula, and, for any given group \Gamma, the contribution of those degree p separable extensions of F whose galoisian closure has group \Gamma.Comment: 36 pages; most of the new material has been moved to the new Section

Representations and KK-theory of Discrete Groups

Let $\Gamma$ be a discrete group of finite virtual cohomological dimension with certain finiteness conditions of the type satisfied by arithmetic groups. We define a representation ring for $\Gamma$, determined on its elements of finite order, which is of finite type. Then we determine the contribution of this ring to the topological $K$-theory $K^*(B\Gamma)$, obtaining an exact formula for the difference in terms of the cohomology of the centralizers of elements of finite order in $\Gamma$.Comment: 4 page

Finiteness properties of cubulated groups

We give a generalized and self-contained account of Haglund-Paulin's wallspaces and Sageev's construction of the CAT(0) cube complex dual to a wallspace. We examine criteria on a wallspace leading to finiteness properties of its dual cube complex. Our discussion is aimed at readers wishing to apply these methods to produce actions of groups on cube complexes and understand their nature. We develop the wallspace ideas in a level of generality that facilitates their application. Our main result describes the structure of dual cube complexes arising from relatively hyperbolic groups. Let H_1,...,H_s be relatively quasiconvex codimension-1 subgroups of a group G that is hyperbolic relative to P_1,...,P_r. We prove that G acts relatively cocompactly on the associated dual CAT(0) cube complex C. This generalizes Sageev's result that C is cocompact when G is hyperbolic. When P_1,...,P_r are abelian, we show that the dual CAT(0) cube complex C has a G-cocompact CAT(0) truncation.Comment: 58 pages, 12 figures. Version 3: Revisions and slightly improved results in Sections 7 and 8. Several theorem numbers have changed from the previous versio

Nonlinear Analysis of Irregular Variables

The Fourier spectral techniques that are common in Astronomy for analyzing periodic or multi-periodic light-curves lose their usefulness when they are applied to unsteady light-curves. We review some of the novel techniques that have been developed for analyzing irregular stellar light or radial velocity variations, and we describe what useful physical and astronomical information can be gained from their use.Comment: 31 pages, to appear as a chapter in `Nonlinear Stellar Pulsation' in the Astrophysics and Space Science Library (ASSL), Editors: M. Takeuti & D. Sasselo

TT-adic exponential sums of polynomials in one variable

The $T$-adic exponential sum of a polynomial in one variable is studied. An explicit arithmetic polygon in terms of the highest two exponents of the polynomial is proved to be a lower bound of the Newton polygon of the $C$-function of the T-adic exponential sum. This bound gives lower bounds for the Newton polygon of the $L$-function of exponential sums of $p$-power order

Experience in the exploitation of a large control system

Experience of a four-year exploitation of the large control system of the CERN PS accelerator complex is presented with special emphasis on the parameters which are very sensitive to the exploitation team productivity. The software tools suite used in this daily maintenance is described and a particular analysis of the power and benefits of advance software technology used for the architecture of this suite is explained. The integration of this suite in the Control System is presented, as well as its use in the Control System development phase. Some considerations of the potential benefit of an Object Oriented equipment access are outlined