Diophantine Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Diophantine Geometry write by Marc Hindry. This book was released on 2013-12-01. Diophantine Geometry available in PDF, EPUB and Kindle. This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.
Fundamentals of Diophantine Geometry
Fundamentals of Diophantine Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Fundamentals of Diophantine Geometry write by S. Lang. This book was released on 2013-06-29. Fundamentals of Diophantine Geometry available in PDF, EPUB and Kindle. Diophantine problems represent some of the strongest aesthetic attractions to algebraic geometry. They consist in giving criteria for the existence of solutions of algebraic equations in rings and fields, and eventually for the number of such solutions. The fundamental ring of interest is the ring of ordinary integers Z, and the fundamental field of interest is the field Q of rational numbers. One discovers rapidly that to have all the technical freedom needed in handling general problems, one must consider rings and fields of finite type over the integers and rationals. Furthermore, one is led to consider also finite fields, p-adic fields (including the real and complex numbers) as representing a localization of the problems under consideration. We shall deal with global problems, all of which will be of a qualitative nature. On the one hand we have curves defined over say the rational numbers. Ifthe curve is affine one may ask for its points in Z, and thanks to Siegel, one can classify all curves which have infinitely many integral points. This problem is treated in Chapter VII. One may ask also for those which have infinitely many rational points, and for this, there is only Mordell's conjecture that if the genus is :;;; 2, then there is only a finite number of rational points.
Heights in Diophantine Geometry
Heights in Diophantine Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Heights in Diophantine Geometry write by Enrico Bombieri. This book was released on 2006. Heights in Diophantine Geometry available in PDF, EPUB and Kindle. This monograph is a bridge between the classical theory and modern approach via arithmetic geometry.
Logarithmic Forms and Diophantine Geometry
Logarithmic Forms and Diophantine Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Logarithmic Forms and Diophantine Geometry write by A. Baker. This book was released on 2008-01-17. Logarithmic Forms and Diophantine Geometry available in PDF, EPUB and Kindle. There is now much interplay between studies on logarithmic forms and deep aspects of arithmetic algebraic geometry. New light has been shed, for instance, on the famous conjectures of Tate and Shafarevich relating to abelian varieties and the associated celebrated discoveries of Faltings establishing the Mordell conjecture. This book gives an account of the theory of linear forms in the logarithms of algebraic numbers with special emphasis on the important developments of the past twenty-five years. The first part covers basic material in transcendental number theory but with a modern perspective. The remainder assumes some background in Lie algebras and group varieties, and covers, in some instances for the first time in book form, several advanced topics. The final chapter summarises other aspects of Diophantine geometry including hypergeometric theory and the André-Oort conjecture. A comprehensive bibliography rounds off this definitive survey of effective methods in Diophantine geometry.
O-Minimality and Diophantine Geometry
O-Minimality and Diophantine Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook O-Minimality and Diophantine Geometry write by G. O. Jones. This book was released on 2015-08-13. O-Minimality and Diophantine Geometry available in PDF, EPUB and Kindle. This book brings the researcher up to date with recent applications of mathematical logic to number theory.
