Torsors and Rational Points - 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 Torsors and Rational Points write by Alexei Skorobogatov. This book was released on 2001-07-05. Torsors and Rational Points available in PDF, EPUB and Kindle. This book, first published in 2001, is a complete and coherent exposition of the theory and applications of torsors to rational points.
Torsors, Étale Homotopy and Applications to Rational Points
Torsors, Étale Homotopy and Applications to Rational Points - 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 Torsors, Étale Homotopy and Applications to Rational Points write by Alexei Skorobogatov. This book was released on 2013-04-18. Torsors, Étale Homotopy and Applications to Rational Points available in PDF, EPUB and Kindle. Lecture notes and research articles on the use of torsors and étale homotopy in algebraic and arithmetic geometry.
Rational Points on Varieties
Rational Points on Varieties - 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 Rational Points on Varieties write by Bjorn Poonen. This book was released on 2017-12-13. Rational Points on Varieties available in PDF, EPUB and Kindle. This book is motivated by the problem of determining the set of rational points on a variety, but its true goal is to equip readers with a broad range of tools essential for current research in algebraic geometry and number theory. The book is unconventional in that it provides concise accounts of many topics instead of a comprehensive account of just one—this is intentionally designed to bring readers up to speed rapidly. Among the topics included are Brauer groups, faithfully flat descent, algebraic groups, torsors, étale and fppf cohomology, the Weil conjectures, and the Brauer-Manin and descent obstructions. A final chapter applies all these to study the arithmetic of surfaces. The down-to-earth explanations and the over 100 exercises make the book suitable for use as a graduate-level textbook, but even experts will appreciate having a single source covering many aspects of geometry over an unrestricted ground field and containing some material that cannot be found elsewhere.
Torsors, Étale Homotopy and Applications to Rational Points
Torsors, Étale Homotopy and Applications to Rational Points - 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 Torsors, Étale Homotopy and Applications to Rational Points write by Alexei N. Skorobogatov. This book was released on 2013-04-18. Torsors, Étale Homotopy and Applications to Rational Points available in PDF, EPUB and Kindle. Torsors, also known as principal bundles or principal homogeneous spaces, are ubiquitous in mathematics. The purpose of this book is to present expository lecture notes and cutting-edge research papers on the theory and applications of torsors and étale homotopy, all written from different perspectives by leading experts. Part one of the book contains lecture notes on recent uses of torsors in geometric invariant theory and representation theory, plus an introduction to the étale homotopy theory of Artin and Mazur. Part two of the book features a milestone paper on the étale homotopy approach to the arithmetic of rational points. Furthermore, the reader will find a collection of research articles on algebraic groups and homogeneous spaces, rational and K3 surfaces, geometric invariant theory, rational points, descent and the Brauer–Manin obstruction. Together, these give a state-of-the-art view of a broad area at the crossroads of number theory and algebraic geometry.
Rational Points and Arithmetic of Fundamental Groups
Rational Points and Arithmetic of Fundamental Groups - 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 Rational Points and Arithmetic of Fundamental Groups write by Jakob Stix. This book was released on 2012-10-19. Rational Points and Arithmetic of Fundamental Groups available in PDF, EPUB and Kindle. The section conjecture in anabelian geometry, announced by Grothendieck in 1983, is concerned with a description of the set of rational points of a hyperbolic algebraic curve over a number field in terms of the arithmetic of its fundamental group. While the conjecture is still open today in 2012, its study has revealed interesting arithmetic for curves and opened connections, for example, to the question whether the Brauer-Manin obstruction is the only one against rational points on curves. This monograph begins by laying the foundations for the space of sections of the fundamental group extension of an algebraic variety. Then, arithmetic assumptions on the base field are imposed and the local-to-global approach is studied in detail. The monograph concludes by discussing analogues of the section conjecture created by varying the base field or the type of variety, or by using a characteristic quotient or its birational analogue in lieu of the fundamental group extension.
