(redige par un groupe d'auditeurs)
Augmente d'un expose de Mme Michele Raynaud
Documents Mathematiques 4 (2005), x+208 pages
Resume :
Ce volume est une edition recomposee et annotee du livre ≪
Cohomologie locale des faisceaux coherents et theoremes de
Lefschetz locaux et globaux (SGA 2) ≫ , Advanced Studies in
Pure Mathematics 2, North-Holland Publishing Company - Amsterdam,
1968, par A. Grothendieck et al.
Dans cet ouvrage, on donne des conditions necessaires et
suffisantes de finitude des faisceaux de cohomologie locale d'un
faisceau coherent. Ces resultats conduisent a des theoremes
d'algebrisation qui permettent en particulier d'obtenir, a l'aide
de theoremes de purete egalement demontres dans le texte, des
theoremes de type Lefschetz pour le groupe fondamental ou de
Picard.
Mots clefs : Algebrisation, theoreme de Lefschetz, dualite
locale, cohomologie locale, profondeur, profondeur homotopique,
groupe fondamental, groupe de Picard
Abstract:
Cohomologie locale des faisceaux coherents (SGA 2)
This volume is a new updated edition of the book ``Cohomologie
locale des faisceaux coherents et theoremes de Lefschetz locaux
et globaux (SGA 2)'', Advanced Studies in Pure Mathematics 2,
North-Holland Publishing Company - Amsterdam, 1968, by A.
Grothendieck et al.
In this monograph are given necessary and sufficient conditions
for the finiteness of the local cohomology sheaves of coherent
sheaves. These results provide algebraization theorems leading in
particular, with the help of purity results also proved in the
text, to Lefschetz's theorem for both the fundamental group and
the Picard group.
Key words: Algebraization, Lefschetz's theorem, local duality,
local cohomology, depth, homotopical depth, fundamental group,
Picard group
Class. math. : 14-02, 14B10, 14B15, 14B20, 14C22, 14J70, 32S20
ISBN : 2-85629-169-4
Asterisque 299 (2005), x+350 pages
Resume :
Comme les precedents volumes de ce seminaire, celui-ci contient
quatorze exposes de synthese sur des sujets d'actualite: trois
exposes de geometrie algebrique, quatre sur les equations aux
derivees partielles, un de probabilites, un de theorie des
nombres, un sur les systemes dynamiques, un sur les algebres
d'operateurs, un sur les inegalites geometriques, un de theorie
des representations des groupes et un d'analyse harmonique.
Abstract:
Seminaire Bourbaki, volume 2003/2004, exposes 924-937
As in the preceding volumes of this seminar, one finds here
fourteen survey lectures on topics of current interest: three
lectures on algebraic geometry, four on partial differential
equations, one on probability, one on number theory, one on
dynamical systems, one on operator algebras, one on geometric
inequalities, one on the representation theory of groups and one
on harmonic analysis.
ISBN : 2-85629-173-2
Asterisque 300 (2005), vi+208 pages
Resume :
D-modules avec structure de twisteur polarisable
Nous montrons un theoreme de decomposition pour l'image directe
d'un systeme local irreductible sur une variete projective
complexe lisse par un morphisme a valeurs dans une autre variete
projective complexe lisse. A cet effet, nous construisons une
categorie de -modules avec structure de twisteur polarisee et
nous montrons un theoreme de decomposition dans cette categorie.
Mots clefs : Structure de twisteur, D-module, specialisation,
polarisation, poids
Abstract:
We prove a Decomposition Theorem for the direct image of an
irreducible local system on a smooth complex projective variety
under a morphism with values in another smooth complex projective
variety. For this purpose, we construct a category of polarized
twistor -modules and show a Decomposition Theorem in this
category.
Key words: Twistor structure, D-module, specialization,
polarization, weight
Class. math. : 32S40
ISBN : 2-85629-174-0
Paper | November 2005 | ISBN: 0-691-12330-6
Cloth | November 2005 | ISBN: 0-691-12329-2
448 pp. | 7 x 10
(AM-159)
It is now some thirty years since Deligne first proved his
general equidistribution theorem, thus establishing the
fundamental result governing the statistical properties of
suitably "pure" algebro-geometric families of character
sums over finite fields (and of their associated L-functions).
Roughly speaking, Deligne showed that any such family obeys a
"generalized Sato-Tate law," and that figuring out
which generalized Sato-Tate law applies to a given family amounts
essentially to computing a certain complex semisimple (not
necessarily connected) algebraic group, the "geometric
monodromy group" attached to that family.
Up to now, nearly all techniques for determining geometric
monodromy groups have relied, at least in part, on local
information. In Moments, Monodromy, and Perversity, Nicholas Katz
develops new techniques, which are resolutely global in nature.
They are based on two vital ingredients, neither of which existed
at the time of Deligne's original work on the subject. The first
is the theory of perverse sheaves, pioneered by Goresky and
MacPherson in the topological setting and then brilliantly
transposed to algebraic geometry by Beilinson, Bernstein,
Deligne, and Gabber. The second is Larsen's Alternative, which
very nearly characterizes classical groups by their fourth
moments. These new techniques, which are of great interest in
their own right, are first developed and then used to calculate
the geometric monodromy groups attached to some quite specific
universal families of (L-functions attached to) character sums
over finite fields.
Nicholas M. Katz is Professor of Mathematics at Princeton
University. He is the author of five previous books in this
series: Arithmetic Moduli of Elliptic Curves (with Barry Mazur);
Gauss Sums, Kloosterman Sums, and Monodromy Groups; Exponential
Sums and Differential Equations; Rigid Local Systems; and Twisted
L-Functions and Monodromy.
Table of Contents:
Introduction 1
Chapter 1: Basic results on perversity and higher moments 9
Chapter 2: How to apply the results of Chapter 2 93
Chapter 3: Additive character sums on An 111
Chapter 4: Additive character sums on more general X 161
Chapter 5: Multiplicative character sums on An 185
Chapter 6: Middle addivitve convolution 221
Appendix A6: Swan-minimal poles 281
Chapter 7: Pullbacks to curves from A1 295
Chapter 8: One variable twists on curves 321
Chapter 9: Weierstrass sheaves as inputs 327
Chapter 10: Weirstrass families 349
Chapter 11: FJTwist families and variants 371
Chapter 12: Uniformity results 407
Chapter 13: Average analytic rank and large N limits 443
References 455
Notation Index 461
Subject Index 467
Series: Cambridge Monographs on Mathematical Physics
Paperback (ISBN-10: 0521020042 | ISBN-13: 9780521020046)
Published September 2005 | 475 pages | 247 x 174 mm
This book is an introduction to integrability and conformal field
theory in two dimensions using quantum groups. The book begins
with a brief introduction to S-matrices, spin chains and vertex
models as a prelude to the study of Yang?Baxter algebras and the
Bethe ansatz. The basic ideas of integrable systems are then
introduced, giving particular emphasis to vertex and face models.
Special attention is given to explaining the underlying
mathematical tools, including braid groups, knot invariants and
towers of algebra. The book then goes on to give a detailed
introduction to quantum groups as a prelude to chapters on
integrable models, two-dimensional conformal field theories and
superconformal field theories. The book contains many diagrams
and exercises to illustrate key points in the text.
* Quantum groups of great current interest
* Special emphasis on explaining underlying mathematical tools
* One of the few books available that show applications in
physics
* Highly illustrated to explain key concepts
Contents
Preface; 1. S-matrices, spin chains and vertex models; 2. The
Yang?Baxter equation ? a first look; 3. Bethe ansatz ? some
examples; 4. The eight-vertex model; 5. Face models; 6. Quantum
groups ? mathematical review; 7. Integrable models at roots of
unit; 8. Two-dimensional conformal field theories; 9. Duality in
conformal field theories; 10. Coulomb gas representation; 11.
Quantum groups in conformal field theory.
Hardback (ISBN-10: 0521848059 | ISBN-13: 9780521848053)
Published July 2005 | 1056 pages | 253 x 177 mm
Courses: econometrics, microeconometrics, applied economics,
statistics, applied mathematics
Levels: FINAL-YEAR UNDERGRADUATES AND ABOVE
This book provides the most comprehensive treatment to date of
microeconometrics, the analysis of individual-level data on the
economic behavior of individuals or firms using regression
methods for cross section and panel data. The book is oriented to
the practitioner. A basic understanding of the linear regression
model with matrix algebra is assumed. The text can be used for a
microeconometrics course, typically a second-year economics PhD
course; for data-oriented applied microeconometrics field
courses; and as a reference work for graduate students and
applied researchers who wish to fill in gaps in their toolkit.
Distinguishing features of the book include emphasis on nonlinear
models and robust inference, simulation-based estimation, and
problems of complex survey data. The book makes frequent use of
numerical examples based on generated data to illustrate the key
models and methods. More substantially, it systematically
integrates into the text empirical illustrations based on seven
large and exceptionally rich data sets.
* Most comprehensive text on microeconometrics available anywhere
* Authors are leading experts on the subject matter
* Self-contained, rich with exercises, perennially important
subject
Contents
1. Introduction; 2. Causal and non-causal models; 3.
Microeconomic data structures; 4. Linear models; 5. ML and NLS
estimation; 6. GMM and systems estimation; 7. Hypothesis tests; 8.
Specification tests and model selection; 9. Semiparametric
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Simulation-based methods; 13. Bayesian methods; 14. Binary
outcome models; 15. Multinomial models; 16. Tobit and selection
models; 17. Transition data: survival analysis; 18. Mixture
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hazards; 20. Models of count data; 21. Linear panel models:
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models; 24. Stratified and clustered samples; 25. Treatment
evaluation; 26. Measurement error models; 27. Missing data and
imputation; A. Asymptotic theory; B. Making pseudo-random draw.
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Amsterdam, The Netherlands