书目名称 | Notes on Geometry and Arithmetic |
编辑 | Daniel Coray |
视频video | http://file.papertrans.cn/669/668254/668254.mp4 |
概述 | Offers readers a ‘hands on’ introduction to Diophantine geometry.Progresses from introductory to advanced topics using the language of classical geometry.Assumes only modest prerequisites in abstract |
丛书名称 | Universitext |
图书封面 |  |
描述 | .This English translation of Daniel Coray’s original French textbook. Notes de géométrie et d’arithmétique. introduces students to Diophantine geometry. It engages the reader with concrete and interesting problems using the language of classical geometry, setting aside all but the most essential ideas from algebraic geometry and commutative algebra. Readers are invited to discover rational points on varieties through an appealing ‘hands on’ approach that offers a pathway toward active research in arithmetic geometry. Along the way, the reader encounters the state of the art on solving certain classes of polynomial equations with beautiful geometric realizations, and travels a unique ascent towards variations on the Hasse Principle..Highlighting the importance of Diophantus of Alexandria as a precursor to the study of arithmetic over the rational numbers, this textbook introduces basic notions with an emphasis on Hilbert’s Nullstellensatz over an arbitrary field. A digression on Euclidian rings is followed by a thorough study of the arithmetic theory of cubic surfaces. Subsequent chapters are devoted to p-adic fields, the Hasse principle, and the subtle notion of Diophantine dimensi |
出版日期 | Textbook 2020 |
关键词 | algebraic varieties; rational points; cubic surfaces; Hasse principle; Diophantine dimension of a field |
版次 | 1 |
doi | https://doi.org/10.1007/978-3-030-43781-7 |
isbn_softcover | 978-3-030-43780-0 |
isbn_ebook | 978-3-030-43781-7Series ISSN 0172-5939 Series E-ISSN 2191-6675 |
issn_series | 0172-5939 |
copyright | Springer Nature Switzerland AG 2020 |