General Galois Geometries

Author : James Hirschfeld
Publisher : Springer
ISBN 13 : 1447167902
Total Pages : 409 pages
Book Rating : 4.07/5 ( download)

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Download or read book General Galois Geometries written by James Hirschfeld and published by Springer. This book was released on 2016-02-03 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 :
ISBN 13 : 9780198538370
Total Pages : 0 pages
Book Rating : 4.75/5 ( download)

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Download or read book General Galois Geometries written by James William Peter Hirschfeld and published by . This book was released on 1991 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : James William Peter Hirschfeld
Publisher : Oxford University Press on Demand
ISBN 13 : 9780198502951
Total Pages : 555 pages
Book Rating : 4.58/5 ( download)

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Download or read book Projective Geometries Over Finite Fields written by James William Peter Hirschfeld and published by Oxford University Press on Demand. This book was released on 1998 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
ISBN 13 : 1139493442
Total Pages : 91 pages
Book Rating : 4.44/5 ( download)

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Download or read book Dynamics, Statistics and Projective Geometry of Galois Fields written by V. I. Arnold and published by Cambridge University Press. This book was released on 2010-12-02 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Serge Lang
Publisher : Courier Dover Publications
ISBN 13 : 048683980X
Total Pages : 273 pages
Book Rating : 4.06/5 ( download)

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Download or read book Introduction to Algebraic Geometry written by Serge Lang and published by Courier Dover Publications. This book was released on 2019-03-20 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
ISBN 13 : 9781620813638
Total Pages : 284 pages
Book Rating : 4.37/5 ( download)

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Download or read book Current Research Topics on Galois Geometry written by Leo Storme and published by Nova Science Publishers. This book was released on 2014-05-14 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
ISBN 13 : 0521644194
Total Pages : 506 pages
Book Rating : 4.98/5 ( download)

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Download or read book Galois Representations in Arithmetic Algebraic Geometry written by A. J. Scholl and published by Cambridge University Press. This book was released on 1998-11-26 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conference proceedings based on the 1996 LMS Durham Symposium 'Galois representations in arithmetic algebraic geometry'.

Author : Stephen C. Newman
Publisher : John Wiley & Sons
ISBN 13 : 1119517532
Total Pages : 656 pages
Book Rating : 4.35/5 ( download)

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Download or read book Semi-Riemannian Geometry written by Stephen C. Newman and published by John Wiley & Sons. This book was released on 2019-07-30 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Harald Niederreiter
Publisher : Princeton University Press
ISBN 13 : 140083130X
Total Pages : 272 pages
Book Rating : 4.02/5 ( download)

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Download or read book Algebraic Geometry in Coding Theory and Cryptography written by Harald Niederreiter and published by Princeton University Press. This book was released on 2009-09-21 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook equips graduate students and advanced undergraduates with the necessary theoretical tools for applying algebraic geometry to information theory, and it covers primary applications in coding theory and cryptography. Harald Niederreiter and Chaoping Xing provide the first detailed discussion of the interplay between nonsingular projective curves and algebraic function fields over finite fields. This interplay is fundamental to research in the field today, yet until now no other textbook has featured complete proofs of it. Niederreiter and Xing cover classical applications like algebraic-geometry codes and elliptic-curve cryptosystems as well as material not treated by other books, including function-field codes, digital nets, code-based public-key cryptosystems, and frameproof codes. Combining a systematic development of theory with a broad selection of real-world applications, this is the most comprehensive yet accessible introduction to the field available. Introduces graduate students and advanced undergraduates to the foundations of algebraic geometry for applications to information theory Provides the first detailed discussion of the interplay between projective curves and algebraic function fields over finite fields Includes applications to coding theory and cryptography Covers the latest advances in algebraic-geometry codes Features applications to cryptography not treated in other books

Author : David Eisenbud
Publisher : Springer Science & Business Media
ISBN 13 : 0387226397
Total Pages : 265 pages
Book Rating : 4.92/5 ( download)

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Download or read book The Geometry of Schemes written by David Eisenbud and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.