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.
The Arithmetic of Fundamental Groups
The 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 The Arithmetic of Fundamental Groups write by Jakob Stix. This book was released on 2012-01-10. The Arithmetic of Fundamental Groups available in PDF, EPUB and Kindle. In the more than 100 years since the fundamental group was first introduced by Henri Poincaré it has evolved to play an important role in different areas of mathematics. Originally conceived as part of algebraic topology, this essential concept and its analogies have found numerous applications in mathematics that are still being investigated today, and which are explored in this volume, the result of a meeting at Heidelberg University that brought together mathematicians who use or study fundamental groups in their work with an eye towards applications in arithmetic. The book acknowledges the varied incarnations of the fundamental group: pro-finite, l-adic, p-adic, pro-algebraic and motivic. It explores a wealth of topics that range from anabelian geometry (in particular the section conjecture), the l-adic polylogarithm, gonality questions of modular curves, vector bundles in connection with monodromy, and relative pro-algebraic completions, to a motivic version of Minhyong Kim's non-abelian Chabauty method and p-adic integration after Coleman. The editor has also included the abstracts of all the talks given at the Heidelberg meeting, as well as the notes on Coleman integration and on Grothendieck's fundamental group with a view towards anabelian geometry taken from a series of introductory lectures given by Amnon Besser and Tamás Szamuely, respectively.
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.
Galois Groups and Fundamental Groups
Galois Groups and 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 Galois Groups and Fundamental Groups write by Tamás Szamuely. This book was released on 2009-07-16. Galois Groups and Fundamental Groups available in PDF, EPUB and Kindle. Assuming little technical background, the author presents the strong analogies between these two concepts starting at an elementary level.
Arithmetic Fundamental Groups and Noncommutative Algebra
Arithmetic Fundamental Groups and Noncommutative Algebra - 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 Arithmetic Fundamental Groups and Noncommutative Algebra write by Michael D. Fried. This book was released on 2002. Arithmetic Fundamental Groups and Noncommutative Algebra available in PDF, EPUB and Kindle. The arithmetic and geometry of moduli spaces and their fundamental groups are a very active research area. This book offers a complete overview of developments made over the last decade. The papers in this volume examine the geometry of moduli spaces of curves with a function on them. The main players in Part 1 are the absolute Galois group $G {\mathbb Q $ of the algebraic numbers and its close relatives. By analyzing how $G {\mathbb Q $ acts on fundamental groups defined by Hurwitz moduli problems, the authors achieve a grand generalization of Serre's program from the 1960s. Papers in Part 2 apply $\theta$-functions and configuration spaces to the study of fundamental groups over positive characteristic fields. In this section, several authors use Grothendieck's famous lifting results to give extensions to wildly ramified covers. Properties of the fundamental groups have brought collaborations between geometers and group theorists. Several Part 3 papers investigate new versions of the genus 0 problem. In particular, this includes results severely limiting possible monodromy groups of sphere covers. Finally, Part 4 papers treat Deligne's theory of Tannakian categories and arithmetic versions of the Kodaira-Spencer map. This volume is geared toward graduate students and research mathematicians interested in arithmetic algebraic geometry.
