In this volume the author gives a unified presentation of some of the basic tools and concepts in number theory, commutative algebra, and algebraic geometry, and for the first time in a book at this level, brings out the deep analogies between them. The geometric viewpoint is stressed throughout the book. Extensive examples are given to illustrate each new concept, and many interesting exercises are given at the end of each chapter. Most of the important results in the one-dimensional case are proved, including Bombieri's proof of the Riemann Hypothesis for curves over a finite field. While the book is not intended to be an introduction to schemes, the author indicates how many of the geometric notions introduced in the book relate to schemes which will aid the reader who goes to the next level of this rich subject.

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"Extremely carefully written, masterfully thought out, and skillfully arranged introduction ... to the arithmetic of algebraic curves, on the one hand, and to the algebro-geometric aspects of number theory, on the other hand. Detailed discussions, full proofs, much effort at thorough motivations, a wealth of illustrating examples, numerous related exercises and problems, hints for further reading, and a rich bibliography characterize this text as an excellent guide for beginners in arithmetic geometry, just as an interesting reference and methodical inspiration for teachers of the subject ... a highly welcome addition to the existing literature." -- *Zentralblatt fr Mathematik*

"In order to come straight to the point: this book represents an excellent introduction to Algebraic Number Theory and to Algebraic Curves as well by viewing both theories as part of Commutative Algebra ... all proof are given in full detail and its concept as well thought-out." --*Monatshefte fr Mathematik*

"In order to come straight to the point: this book represents an excellent introduction to Algebraic Number Theory and to Algebraic Curves as well by viewing both theories as part of Commutative Algebra ... all proof are given in full detail and its concept as well thought-out." ---- Monatshefte für Mathematik

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**Book Description **American Mathematical Society, United States, 1996. Hardback. Book Condition: New. Language: English . Brand New Book. In this volume the author gives a unified presentation of some of the basic tools and concepts in number theory, commutative algebra, and algebraic geometry, and for the first time in a book at this level, brings out the deep analogies between them. The geometric viewpoint is stressed throughout the book. Extensive examples are given to illustrate each new concept, and many interesting exercises are given at the end of each chapter. Most of the important results in the one-dimensional case are proved, including Bombieri s proof of the Riemann Hypothesis for curves over a finite field. While the book is not intended to be an introduction to schemes, the author indicates how many of the geometric notions introduced in the book relate to schemes which will aid the reader who goes to the next level of this rich subject. Bookseller Inventory # AAN9780821802670

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Published by
American Mathematical Society, United States
(1996)

ISBN 10: 0821802674
ISBN 13: 9780821802670

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**Book Description **American Mathematical Society, United States, 1996. Hardback. Book Condition: New. Language: English . Brand New Book. In this volume the author gives a unified presentation of some of the basic tools and concepts in number theory, commutative algebra, and algebraic geometry, and for the first time in a book at this level, brings out the deep analogies between them. The geometric viewpoint is stressed throughout the book. Extensive examples are given to illustrate each new concept, and many interesting exercises are given at the end of each chapter. Most of the important results in the one-dimensional case are proved, including Bombieri s proof of the Riemann Hypothesis for curves over a finite field. While the book is not intended to be an introduction to schemes, the author indicates how many of the geometric notions introduced in the book relate to schemes which will aid the reader who goes to the next level of this rich subject. Bookseller Inventory # AAN9780821802670

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Published by
American Mathematical Society
(1996)

ISBN 10: 0821802674
ISBN 13: 9780821802670

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**Book Description **American Mathematical Society, 1996. Hardcover. Book Condition: New. book. Bookseller Inventory # M0821802674

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**Book Description **Amer Mathematical Society, 1996. Hardcover. Book Condition: Brand New. 397 pages. 10.50x7.50x1.00 inches. In Stock. Bookseller Inventory # __0821802674

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Published by
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**Book Description **American Mathematical Society, 1996. Hardcover. Book Condition: New. Never used!. Bookseller Inventory # P110821802674

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Published by
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ISBN 13: 9780821802670

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**Book Description **American Mathematical Society, 1996. Hardcover. Book Condition: New. Bookseller Inventory # DADAX0821802674

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