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.
| |||||||||||||||
Book Description
Editorial Reviews
Review
"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<br /><br />"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
"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
Product Details
Would you like to update product info or give feedback on images?
|
More About the Author
Discover books, learn about writers, read author blogs, and more.
Customer Reviews
|
There are no customer reviews yet.
|
|||
|
Video reviews
|
Inside This Book
(learn more)
Key Phrases - Statistically Improbable Phrases (SIPs):
(learn more)
nonsingular complete curve, local principal ideal domain, nonsingular affine curve, archimedian absolute values, surjective valuations, plane projective curve, absolutely irreducible polynomial, maximal separable extension, nonsingular plane curve, nonconstant morphism, integral closure, nonsingular curve, irreducible homogeneous polynomial, separable morphism, many maximal ideals, map deg, discriminant ideal, distinct maximal ideals, nonsingular projective curve, residue field extensions, squarefree polynomial, map div, factorial domain, denote the minimal polynomial, nonsingular point Key Phrases - Capitalized Phrases (CAPs): (learn more)
Let Elk, Hilbert's Basis Theorem, Chinese Remainder Theorem, Fermat's Last Theorem, Riemann's Theorem, Introduction Let, Zorn's Lemma, Dirichlet's Unit Theorem, Noether's Normalization Lemma New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
nonsingular complete curve, local principal ideal domain, nonsingular affine curve, archimedian absolute values, surjective valuations, plane projective curve, absolutely irreducible polynomial, maximal separable extension, nonsingular plane curve, nonconstant morphism, integral closure, nonsingular curve, irreducible homogeneous polynomial, separable morphism, many maximal ideals, map deg, discriminant ideal, distinct maximal ideals, nonsingular projective curve, residue field extensions, squarefree polynomial, map div, factorial domain, denote the minimal polynomial, nonsingular point Key Phrases - Capitalized Phrases (CAPs): (learn more)
Let Elk, Hilbert's Basis Theorem, Chinese Remainder Theorem, Fermat's Last Theorem, Riemann's Theorem, Introduction Let, Zorn's Lemma, Dirichlet's Unit Theorem, Noether's Normalization Lemma New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 41
books:
See all 41 books this book cites
- Algebraic Geometry by Shreeram S. Abhyankar in Back Matter (1), and Back Matter (2)
- Algebraic Number Theory (Cambridge Studies in Advanced Mathematics) by A. Fröhlich in Back Matter
- Local Rings (Tracts in Pure & Applied Mathematics) by M. Nagata in Back Matter
- Abelian Varieties (Tata Institute of Fundamental Research, Bombay// Studies in Mathematics) by David Mumford in Back Matter
- Algebraic Geometry (Graduate Texts in Mathematics) by Robin Hartshorne in Back Matter
See all 41 books this book cites
Books on Related Topics
(learn more)
|
What Other Items Do Customers Buy After Viewing This Item?
Suggested Tags from Similar Products(What's this?)Be the first one to add a relevant tag (keyword that's strongly related to this product).
|
Sell a Digital Version of This Book in the Kindle Store
If you are a publisher or author and hold the digital rights to a book, you can sell a digital version of it in our Kindle Store.
Learn more
Customer Discussions
|
This product's forum
Active discussions in related forums
Search Customer Discussions
|
Related forums
|
Listmania!
|
|
