Memoires de la Societe Mathematique de France, Number: 130/131
2012; 250 pp; softcover
ISBN-13: 978-2-85629-376-8
Expected publication date is December 24, 2013.
The author constructs a theory of weights on the rigid cohomology of a separated scheme of finite type over a perfect field of characteristic p>0 by using the log crystalline cohomology of a split proper hypercovering of the scheme. The author also calculates the slope filtration on the rigid cohomology by using the cohomology of the log de Rham-Witt complex of the hypercovering.
A publication of the Societe Mathematique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
Graduate students and research mathematicians interested in rigid cohomology.
*Introduction
*Part I. Weight filtration on the log crystalline cohomology of a simplicial family of open smooth varieties in characteristic p>0*Part II. Weight filtration and slope filtration on the rigid cohomology of a separated scheme of finite type over a perfect field of characteristic p>0*Part III. Weight filtrations and slope filtrations on rigid cohomologies with closed support and with compact support
*Bibliography
Seminaires et Congres, Number: 27
2013; 247 pp; softcover
ISBN-13: 978-2-85629-364-5
Expected publication date is December 24, 2013.
On March 29-April 2, 2010, a meeting was organized at the Luminy CIRM (France) on geometric and differential Galois theories, to recognize the close ties these theories have woven in recent years. This volume contains the proceedings of this meeting. Although it may be viewed as a continuation of the meeting held six years earlier on arithmetic and differential Galois groups (see Groups de Galois Arithmetiques et Differentiels, Seminaires et Congres, volume 13), several new and promising themes have appeared.
The articles gathered here cover the following topics: moduli spaces of connexions, differential equations and coverings in finite characteristic, liftings, monodromy groups in their various guises (tempered fundamental group, motivic groups, generalized difference Galois groups), and arithmetic applications.
Graduate students and research mathematicians interested in geometric and differential Galois theories.
*L. Bary-Soroker and F. Arno -- Open problems in the theory of ample fields
*A. Buium -- Galois groups arising from arithmetic etale equations
*A. Cadoret -- Motivated cycles under specialization
*A. Cadoret and A. Tamagawa -- Note on torsion conjecture
*F. Heiderich -- Introduction to the Galois theory of Artinian simple module algebras
*E. Lepage -- Tempered fundamental group
*F. Loray, M.-H. Saito, and C. Simpson -- Foliations on the moduli space of connections
*B. Matzat -- Monodromy of Frobenius Modules
*A. Maurischat -- On the finite inverse problem in iterative etale Galois theory
*A. Obus -- Toward Abhyankar's Inertia Conjecture For PSL2(*)*M. Van Der Put -- Families of linear etale equations and the Painleve equations
*M. Wibmer -- On the Galois theory of strongly normal etale and difference extensions
*Annexe A. Programme
*Annexe B. Liste des participants
Seminaires et Congres, Number: 28
2013; 121 pp; softcover
ISBN-13: 978-2-85629-365-2
Expected publication date is December 24, 2013.
This volume contains articles related to the conference Self-Similar Processes and Their Applications, which took place in Angers from July 20-24, 2009. Self-similarity is the property which certain stochastic processes have of preserving their distribution under a time-scale change. This property appears in all areas of probability theory and offers a number of fields of application.
The aim of this conference is to bring together the main representatives of different aspects of self-similarity currently being studied in order to promote exchanges on their recent research and enable them to share their knowledge with young researchers.
*Self-similar Markov processes
*Matrix valued self-similar processes
*Self-similarity, trees, branching and fragmentation
*Fractional and multifractional processes
*Stochastic Lowner evolution
*Self-similarity in finance
The organization of the conference was achieved in cooperation with probabilists and statisticians from the research federation Mathematiques des Pays de la Loire. The ANR Geometrie differentielle stochastique et Auto-similarite, based at the University Toulouse III, and the Franco-Mexican project ECOS-Nord, Etude des processus markoviens auto-similaires also contributed to the organization.
Graduate students and research mathematicians interested in self-similiar processes.
*K. Falconer -- Localisable, multifractional and multistable processes
*A. Echelard, J. L. Vehel, and C. Tricot -- A unified framework for 2-microlocal and large deviation spectra
*M. Maejima and Y. Ueda -- Quasi-selfsimilar additive processes
*P.-O. Amblard, J.-F. Coeurjolly, F. Lavancier, and A. Philippe -- Basic properties of the Multivariate Fractional Brownian Motion
*J. B. Levy and M. S. Taqqu -- On the codifference of linear fractional stable motion
*M. Yor -- On weak and strong Brownian filtrations: definitions and examples
*A. Program
*B. List of participants
*
ISBN: 978-1-118-67919-7
320 pages
March 2014
Written by well-known mathematical problem solvers, Modern Geometry features up-to-date and applicable coverage of the wide spectrum of modern geometry and aids readers in learning the art of logical reasoning, modeling, and proof. With its reader-friendly approach, this undergraduate text features: self-contained coverage of modern geometry, provides a large selection of solved exercises to aid in reader comprehension, contains material that can be tailored for a one-, two-, or three-semester sequence, and provides a wide range of fully worked exercises throughout.
| Preface v PART I EUCLIDEAN GEOMETRY 1 Congruency 3 1.1 Introduction 3 1.2 Congruent Figures 6 1.3 Parallel Lines 12 1.3.1 Angles in a Triangle 13 1.3.2 Thales' Theorem 14 1.3.3 Quadrilaterals 17 1.4 More About Congruency 21 1.5 Perpendiculars and Angle Bisectors 24 1.6 Construction Problems 28 1.6.1 The Method of Loci 31 1.7 Solutions to Selected Exercises 33 1.8 Problems 38 2 Concurrency 41 2.1 Perpendicular Bisectors 41 2.2 Angle Bisectors 43 2.3 Altitudes 46 2.4 Medians 48 2.5 Construction Problems 50 2.6 Solutions to the Exercises 54 2.7 Problems 56 3 Similarity 59 3.1 Similar Triangles 59 3.2 Parallel Lines and Similarity 60 3.3 Other Conditions Implying Similarity 64 3.4 Examples 67 3.5 Construction Problems 75 3.6 The Power of a Point 82 3.7 Solutions to the Exercises 87 3.8 Problems 90 4 Theorems of Ceva and Menelaus 95 4.1 Directed Distances, Directed Ratios 95 4.2 The Theorems 97 4.3 Applications of Ceva's Theorem 99 4.4 Applications of Menelaus' Theorem 103 4.5 Proofs of the Theorems 115 4.6 Extended Versions of the Theorems 125 4.6.1 Ceva's Theorem in the Extended Plane 127 4.6.2 Menelaus' Theorem in the Extended Plane 129 4.7 Problems 131 5 Area 133 5.1 Basic Properties 133 5.1.1 Areas of Polygons 134 5.1.2 Finding the Area of Polygons 138 5.1.3 Areas of Other Shapes 139 5.2 Applications of the Basic Properties 140 5.3 Other Formulae for the Area of a Triangle 147 5.4 Solutions to the Exercises 153 5.5 Problems 153 6 Miscellaneous Topics 159 6.1 The Three Problems of Antiquity 159 6.2 Constructing Segments of Speci_c Lengths 161 6.3 Construction of Regular Polygons 166 6.3.1 Construction of the Regular Pentagon 168 6.3.2 Construction of Other Regular Polygons 169 6.4 Miquel's Theorem 171 6.5 Morley's Theorem 178 6.6 The Nine-Point Circle 185 6.6.1 Special Cases 188 6.7 The Steiner-Lehmus Theorem 193 6.8 The Circle of Apollonius 197 6.9 Solutions to the Exercises 200 6.10 Problems 201 PART II TRANSFORMATIONAL GEOMETRY 7 The Euclidean Transformations or Isometries 207 7.1 Rotations, Re_ections, and Translations 207 7.2 Mappings and Transformations 211 7.2.1 Isometries 213 7.3 Using Rotations, Re_ections, and Translations 217 7.4 Problems 227 8 The Algebra of Isometries 231 8.1 Basic Algebraic Properties 231 8.2 Groups of Isometries 236 8.2.1 Direct and Opposite Isometries 237 8.3 The Product of Re_ections 241 8.4 Problems 246 9 The Product of Direct Isometries 253 9.1 Angles 253 9.2 Fixed Points 255 9.3 The Product of Two Translations 256 9.4 The Product of a Translation and a Rotation 257 9.5 The Product of Two Rotations 260 9.6 Problems 263 |
10 Symmetry and Groups 269 10.1 More About Groups 269 10.1.1 Cyclic and Dihedral Groups 273 10.2 Leonardo's Theorem 277 10.3 Problems 281 11 Homotheties 287 11.1 The Pantograph 287 11.2 Some Basic Properties 288 11.2.1 Circles 291 11.3 Construction Problems 293 11.4 Using Homotheties in Proofs 298 11.5 Dilatation 302 11.6 Problems 304 12 Tessellations 311 12.1 Tilings 311 12.2 Monohedral Tilings 312 12.3 Tiling with Regular Polygons 317 12.4 Platonic and Archimedean Tilings 323 12.5 Problems 330 PART III INVERSIVE AND PROJECTIVE GEOMETRIES 13 Introduction to Inversive Geometry 337 13.1 Inversion in the Euclidean Plane 337 13.2 The Effect of Inversion on Euclidean Properties 343 13.3 Orthogonal Circles 351 13.4 Compass-Only Constructions 360 13.5 Problems 369 14 Reciprocation and the Extended Plane 373 14.1 Harmonic Conjugates 373 14.2 The Projective Plane and Reciprocation 383 14.3 Conjugate Points and Lines 393 14.4 Conics 399 14.5 Problems 406 15 Cross Ratios 409 15.1 Cross Ratios 409 15.2 Applications of Cross Ratios 420 15.3 Problems 429 16 Introduction to Projective Geometry 433 16.1 Straightedge Constructions 433 16.2 Perspectivities and Projectivities 443 16.3 Line Perspectivities and Line Projectivities 448 16.4 Projective Geometry and Fixed Points 448 16.5 Projecting a Line to In_nity 451 16.6 The Apollonian Definition of a Conic 455 16.7 Problems 461 Bibliography 464 Index 469 |