[PDF] General Galois Geometries eBook

Author : James Hirschfeld
Publisher : Springer
Page : 422 pages
File Size : 38,60 MB
Release : 2016-02-03
Category : Mathematics
ISBN : 1447167902

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This book is the second edition of the third and last volume of a treatise on projective spaces over a finite field, also known as Galois geometries. This volume completes the trilogy comprised of plane case (first volume) and three dimensions (second volume). This revised edition includes much updating and new material. It is a mostly self-contained study of classical varieties over a finite field, related incidence structures and particular point sets in finite n-dimensional projective spaces. General Galois Geometries is suitable for PhD students and researchers in combinatorics and geometry. The separate chapters can be used for courses at postgraduate level.

Author : James William Peter Hirschfeld
Publisher : Oxford University Press on Demand
Page : 555 pages
File Size : 29,46 MB
Release : 1998
Category : Law
ISBN : 9780198502951

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I. Introduction 1. Finite fields 2. Projective spaces and algebraic varieties II. Elementary general properties 3. Subspaces 4. Partitions 5. Canonical forms for varieties and polarities III. The line and the plane 6. The line 7. First properties of the plane 8. Ovals 9. Arithmetic of arcs of degree two 10. Arcs in ovals 11. Cubic curves 12. Arcs of higher degree 13. Blocking sets 14. Small planes Appendix Notation References.

Author : V. I. Arnold
Publisher : Cambridge University Press
Page : 91 pages
File Size : 47,37 MB
Release : 2010-12-02
Category : Mathematics
ISBN : 1139493442

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V. I. Arnold reveals some unexpected connections between such apparently unrelated theories as Galois fields, dynamical systems, ergodic theory, statistics, chaos and the geometry of projective structures on finite sets. The author blends experimental results with examples and geometrical explorations to make these findings accessible to a broad range of mathematicians, from undergraduate students to experienced researchers.

Author : Leo Storme
Publisher : Nova Science Publishers
Page : 0 pages
File Size : 33,79 MB
Release : 2014-05
Category :
ISBN : 9781631173400

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Galois geometry is the theory that deals with substructures living in projective spaces over finite fields, also called Galois fields. This collected work presents current research topics in Galois geometry, and their applications. Presented topics include classical objects, blocking sets and caps in projective spaces, substructures in finite classical polar spaces, the polynomial method in Galois geometry, finite semifields, links between Galois geometry and coding theory, as well as links between Galois geometry and cryptography.

Author : Stephen C. Newman
Publisher : John Wiley & Sons
Page : 656 pages
File Size : 38,23 MB
Release : 2019-07-30
Category : Mathematics
ISBN : 1119517532

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An introduction to semi-Riemannian geometry as a foundation for general relativity Semi-Riemannian Geometry: The Mathematical Language of General Relativity is an accessible exposition of the mathematics underlying general relativity. The book begins with background on linear and multilinear algebra, general topology, and real analysis. This is followed by material on the classical theory of curves and surfaces, expanded to include both the Lorentz and Euclidean signatures. The remainder of the book is devoted to a discussion of smooth manifolds, smooth manifolds with boundary, smooth manifolds with a connection, semi-Riemannian manifolds, and differential operators, culminating in applications to Maxwell’s equations and the Einstein tensor. Many worked examples and detailed diagrams are provided to aid understanding. This book will appeal especially to physics students wishing to learn more differential geometry than is usually provided in texts on general relativity.

Author : Serge Lang
Publisher : Courier Dover Publications
Page : 273 pages
File Size : 36,34 MB
Release : 2019-03-20
Category : Mathematics
ISBN : 048683980X

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Author Serge Lang defines algebraic geometry as the study of systems of algebraic equations in several variables and of the structure that one can give to the solutions of such equations. The study can be carried out in four ways: analytical, topological, algebraico-geometric, and arithmetic. This volume offers a rapid, concise, and self-contained introductory approach to the algebraic aspects of the third method, the algebraico-geometric. The treatment assumes only familiarity with elementary algebra up to the level of Galois theory. Starting with an opening chapter on the general theory of places, the author advances to examinations of algebraic varieties, the absolute theory of varieties, and products, projections, and correspondences. Subsequent chapters explore normal varieties, divisors and linear systems, differential forms, the theory of simple points, and algebraic groups, concluding with a focus on the Riemann-Roch theorem. All the theorems of a general nature related to the foundations of the theory of algebraic groups are featured.

Author : Leo Storme
Publisher : Nova Science Publishers
Page : 284 pages
File Size : 41,27 MB
Release : 2014-05-14
Category : Galois theory
ISBN : 9781620813638

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Galois geometry is the theory that deals with substructures living in projective spaces over finite fields, also called Galois fields. This collected work presents current research topics in Galois geometry, and their applications. Presented topics include classical objects, blocking sets and caps in projective spaces, substructures in finite classical polar spaces, the polynomial method in Galois geometry, finite semifields, links between Galois geometry and coding theory, as well as links between Galois geometry and cryptography. (Imprint: Nova)

Author : A. J. Scholl
Publisher : Cambridge University Press
Page : 506 pages
File Size : 30,5 MB
Release : 1998-11-26
Category : Mathematics
ISBN : 0521644194

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Conference proceedings based on the 1996 LMS Durham Symposium 'Galois representations in arithmetic algebraic geometry'.

Author : David Eisenbud
Publisher : Springer Science & Business Media
Page : 265 pages
File Size : 40,2 MB
Release : 2006-04-06
Category : Mathematics
ISBN : 0387226397

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Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.