Notes on geometry and arithmetic / Daniel Coray.
2020
QA242.5
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Can lend chapters, not whole ebooks
Details
Title
Notes on geometry and arithmetic / Daniel Coray.
Author
Coray, D. F. (Daniel F.)
ISBN
9783030437817 (electronic book)
3030437817 (electronic book)
3030437809
9783030437800
3030437817 (electronic book)
3030437809
9783030437800
Publication Details
Cham : Springer, 2020.
Language
English
Description
1 online resource
Item Number
10.1007/978-3-030-43
Call Number
QA242.5
Dewey Decimal Classification
516.3/5
Summary
This English translation of Daniel Corays original French textbook Notes de géométrie et darithmétique 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 Hilberts 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 dimension of fields. All chapters contain exercises, with hints or complete solutions. Notes on Geometry and Arithmetic will appeal to a wide readership, ranging from graduate students through to researchers. Assuming only a basic background in abstract algebra and number theory, the text uses Diophantine questions to motivate readers seeking an accessible pathway into arithmetic geometry.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Series
Universitext.
Available in Other Form
Print version: 9783030437800
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