springer.com Mathematics : Algebraic Geometry Coray, Daniel Notes on Geometry and Arithmetic 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 algebra and number theory Contains numerous exercises throughout 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 Springer pathway toward active research in arithmetic geometry. Along the way, the reader encounters 1st ed. 2020, XII, 181 p. the state of the art on solving certain classes of polynomial equations with beautiful geometric 1st 121 illus., 3 illus. in color. edition 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 Printed book study of the arithmetic theory of cubic surfaces. Subsequent chapters are devoted to p-adic Softcover fields, the Hasse principle, and the subtle notion of Diophantine dimension of fields. All Printed book chapters contain exercises, with hints or complete solutions. Notes on Geometry and Arithmetic Softcover will appeal to a wide readership, ranging from graduate students through to researchers. ISBN 978-3-030-43780-0 Assuming only a basic background in abstract algebra and number theory, the text uses $ 54,99 Diophantine questions to motivate readers seeking an accessible pathway into arithmetic geometry. Available Discount group Order online at springer.com/booksellers Professional Books (2) Springer Nature Customer Service Center LLC Product category 233 Spring Street Graduate/advanced undergraduate textbook New York, NY 10013 Series USA Universitext T: +1-800-SPRINGER NATURE (777-4643) or 212-460-1500 [email protected] Prices and other details are subject to change without notice. All errors and omissions excepted. Americas: Tax will be added where applicable. Canadian residents please add PST, QST or GST. Please add $5.00 for shipping one book and $ 1.00 for each additional book. Outside the US and Canada add $ 10.00 for first book, $5.00 for each additional book. If an order cannot be fulfilled within 90 days, payment will be refunded upon request. Prices are payable in US currency or its equivalent. ISBN 978-3-030-43780-0 / BIC: PBMW / SPRINGER NATURE: SCM11019 Part of .