東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Notes on geometry and arithmetic

Coray, Daniel.

FindBook

Google Book

Amazon

博客來

Notes on geometry and arithmetic

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Notes on geometry and arithmetic/ by Daniel Coray.
作者:	Coray, Daniel.
出版者:	Cham :Springer International Publishing : : 2020.,
面頁冊數:	xii, 181 p. :ill., digital ;24 cm.
內容註:	Chapter 1. Diophantus of Alexandria -- Chapter 2. Algebraic closure; affine space -- Chapter 3. Rational points; finite fields -- Chapter 4. Projective varieties; conics and quadrics -- Chapter 5. The Nullstellensatz -- Chapter 6. Euclidean rings -- Chapter 7. Cubic surfaces -- Chapter 8. p-adic completions -- Chapter 9. The Hasse principle -- Chapter 10. Diophantine dimension of fields.
Contained By:	Springer Nature eBook
標題:	Arithmetical algebraic geometry. -
電子資源:	https://doi.org/10.1007/978-3-030-43781-7
ISBN:	9783030437817

Notes on geometry and arithmetic
Coray, Daniel.

Notes on geometry and arithmetic[electronic resource] /by Daniel Coray. - Cham :Springer International Publishing :2020. - xii, 181 p. :ill., digital ;24 cm. - Universitext,0172-5939. - Universitext..

Chapter 1. Diophantus of Alexandria -- Chapter 2. Algebraic closure; affine space -- Chapter 3. Rational points; finite fields -- Chapter 4. Projective varieties; conics and quadrics -- Chapter 5. The Nullstellensatz -- Chapter 6. Euclidean rings -- Chapter 7. Cubic surfaces -- Chapter 8. p-adic completions -- Chapter 9. The Hasse principle -- Chapter 10. Diophantine dimension of fields.

This English translation of Daniel Coray's original French textbook Notes de geometrie et d'arithmetique 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 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.

ISBN: 9783030437817

Standard No.: 10.1007/978-3-030-43781-7doiSubjects--Topical Terms:

699672
Arithmetical algebraic geometry.

LC Class. No.: QA242.5 / .C673 2020

Dewey Class. No.: 516.35

Notes on geometry and arithmetic
LDR:02975nmm a2200337 a 4500 001 2222648
003 DE-He213
005 20201117093405.0
006 m d
007 cr nn 008maaau
008 210108s2020 sz s 0 eng d
020 $a 9783030437817 $q (electronic bk.)
020 $a 9783030437800 $q (paper)
024 7 $a 10.1007/978-3-030-43781-7 $2 doi
035 $a 978-3-030-43781-7
040 $a GP $c GP
041 0 $a eng
050 4 $a QA242.5 $b .C673 2020
072 7 $a PBMW $2 bicssc
072 7 $a MAT012010 $2 bisacsh
072 7 $a PBMW $2 thema
082 0 4 $a 516.35 $2 23
090 $a QA242.5 $b .C788 2020
100 1 $a Coray, Daniel. $3 3461596
245 1 0 $a Notes on geometry and arithmetic $h [electronic resource] / $c by Daniel Coray.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2020.
300 $a xii, 181 p. : $b ill., digital ; $c 24 cm.
490 1 $a Universitext, $x 0172-5939
505 0 $a Chapter 1. Diophantus of Alexandria -- Chapter 2. Algebraic closure; affine space -- Chapter 3. Rational points; finite fields -- Chapter 4. Projective varieties; conics and quadrics -- Chapter 5. The Nullstellensatz -- Chapter 6. Euclidean rings -- Chapter 7. Cubic surfaces -- Chapter 8. p-adic completions -- Chapter 9. The Hasse principle -- Chapter 10. Diophantine dimension of fields.
520 $a This English translation of Daniel Coray's original French textbook Notes de geometrie et d'arithmetique 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 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.
650 0 $a Arithmetical algebraic geometry. $3 699672
650 0 $a Geometry. $3 517251
650 1 4 $a Algebraic Geometry. $3 893861
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Universitext. $3 812115
856 4 0 $u https://doi.org/10.1007/978-3-030-43781-7
950 $a Mathematics and Statistics (SpringerNature-11649)