Table of Contents

Rings and Modules.- The Theory of Noetherian Rings.- Integral Extensions.- Extension of Coefficients and Descent.- Homological Methods: Ext and Tor.- Affine Schemes and Basic Constructions.- Techniques of Global Schemes.- Etale and Smooth Morphisms.- Projective Schemes and Proper Morphisms.

Reviews

From the reviews:“The book under review is a self-contained introduction to both fields and their relationship and is divided into two parts. … The book is well written and there are exercises at the end of the chapter sections. … this is certainly a welcome addition to the library of anyone interested in these fields.” (Cícero Carvalho, Mathematical Reviews, September, 2013)“Bosch (Wilhelms Univ., Westphalia, Germany) offers an introduction to scheme-theoretic algebraic geometry preceded by an extended treatment of the prerequisite commutative algebra. … this is a useful, self-contained work for those interested in studying the modern approach to the subject. Summing Up: Recommended. Graduate students and researchers/faculty.” (S. J. Colley, Choice, Vol. 50 (10), June, 2013)“The book is carefully written, with good examples, detailed proofs, and plenty of exercises at the end of every one of its sections. Each chapter has an introduction where the author discusses informally and motivates the contents of the chapter. I liked the book and I believe that it can be used either as textbook for a two-semester introduction to algebraic geometry or for self-study by a motivated student.” (Felipe Zaldivar, MAA Reviews, March, 2013)“Book under review is to introduce the basic concepts and methods of modern algebraic geometry to novices in the field … . each chapter comes with its own introduction, where the author motivates the respective contents by illustrating examples and spotlights the main aspects. … a useful glossary of notations, a comprehensive index, and a list of hints for further reading facilitate working with this textbook considerably. … the current book is an excellent primer on the elements of modern algebraic geometry and commutative algebra.” (Werner Kleinert, Zentralblatt MATH, Vol. 1257, 2013)