An Invitation to Arithmetic Geometry (Graduate Studies in Mathematics No. 9)
By: Dino Lorenzini (author)Hardback
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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.
Integral closure Plane curves Factorization of ideals The discriminants The ideal class group Projective curves Nonsingular complete curves Zeta-functions The Riemann-Roch Theorem Frobenius morphisms and the Riemann hypothesis Further topics Appendix Glossary of notation Index Bibliography.
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- ID: 9780821802670
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