Prolegomena to a middlebrow arithmetic of curves of genus 2 cassels j w s flynn e v
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The quintic case -- Chapter 7. Abstract: The number theoretic properties of curves of genus 2 are attracting increasing attention. Lecture Notes in Computer Science, Springer-Verlag 3076 2004 , 132139. Number Theory 153 2015 , 270282. The Mordell-Weil group can then be determined for many curves, and in many non-trivial cases all rational points can be found. Algorithms in Algebraic Geometry, L. A worked example of descent via isogeny -- 5.

Number theorists, algebraic geometers and workers in related areas will find that this book offers unique insights into the arithmetic of curves of genus 2. Curves of genus 2 -- Ch. The work is accessible to beginning graduate students in number theory, algebraic geometry and workers in related areas. Contents: Cover -- Title -- Copyright -- Contents -- Foreword -- Background and conventions -- 0. Performing 2-descent without using homogeneous spaces. Category: Computers Author : L. The group law on the jacobian -- 10.

Homogeneous spaces JØd1,d2 and norm spaces LØd1,d2 -- 4. The endomorphism ring -- Ch. The dual of t h e Kummer -- 0. The jacobian as double cover -- 9. Computing the Mordell-Weil group -- 0. Another is an algorithm of Poonen's Computing torsion points on curves for curves over Q.

The E-mail message field is required. Computing the Mordell-Weil group -- Ch. Additional papers have been added which provide some background for readers who were not at the conference, with the intention of making the book logically more complete and easier to read, but familiarity with the basic facts of algebraic geometry, commutative algebra and number theory are assumed. Chevalley; and On the Theory of General Partial Differential Operators by Lars Hormander, reviewed by J. Thanasis Bouganis, Otmar Venjakob, Contributions in Mathematical and Computational Sciences, Vol.

Formal group law -- Appendix I. London Mathematical Society Lecture Note Series 230. Number Theory 186 2018 , 248258. Files available by anonymous ftp. The Kummer formulation -- 5. Change of coordinates on C -- Change of coordinates on C -- Chapter 3. Isogeny for the curve -- Chapter 10.

Ricardo Baeza, Wai Kiu Chan, Detlev W. Recovery of the curve -- Chapter 4. Schoissengeier, Monatshefte fur Mathematik '. The Mordell—Weil group can then be determined for many curves, and in many non-trivial cases all rational points can be found. Description: 1 online resource 236 pages.

Research Interests My main area of research is ; more specifically the arithmetic of , Higher Genus Curves, and especially Jacobians of curves, Chabauty techniques, Visualisation of the Shafarevich-Tate Group, and the Brauer-Manin Obstruction. London Mathematical Society Lecture Note Series, 230. Parshin on the occasion of his 60th birthday, Ed. Searching for large rational torsion -- Chapter 9. Number Theoretic and Algebraic Methods in Computer Science, Alf van der Poorten, Igor Shparlinski and Horst G. The Kummer viewpoint -- 8. Siegel's Über einige Anwendungen diophantischer Approximationen, with a commentary by C.

The number theoretic properties of curves of genus 2 are attracting increasing attention. This book provides new insights into this subject; much of the material here is entirely new, and none has appeared in book form before. Mathematicians can then determine the Mordell-Weil group for many curves, and in many nontrivial cases they can find all rational points. Curves of genus 2 2. Among those reviews, for example, are the following: Homological Algebra by Henri Cartan and Samuel Eilenberg, reviewed by G. A worked example of complete 2-descent -- 4.

The Kummer surface -- 0. The results exemplify the power of computer algebra in diophantine contexts, but computer expertise is not assumed in the main text. The book is divided into three sections. The isogeny on the jacobian variety -- 2. The Kummer surface -- Ch. Finite-dimensional Galois modules -- Finite-dimensional Galois modules -- Chapter 1. Gebhard Böckle, Gabor Wiese, Contributions in Mathematical and Computational Sciences, Vol.

Number Theory 36 1990 , 257265. Williams, London Mathematical Society Student Texts No. The jacobian over local fields; Formal groups; 8. This book provides new insights into this subject; much of the material here is entirely new, and none has appeared in book form before. The dual of the Kummer; 5.