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Goodreads helps you keep track of books you want to read. Want to Read savingâ€¦. Want to Read Currently Reading Read. Other editions. Enlarge cover. Error rating book. Refresh and try again. Open Preview See a Problem? Details if other :. Thanks for telling us about the problem. Return to Book Page. Algebraic geometry is a fascinating branch of mathematics that combines methods from both, algebra and geometry. It transcends the limited scope of pure algebra by means of geometric construction principles.

Moreover, Grothendieck's schemes invented in the late s allowed the application of algebraic-geometric methods in fields that formerly seemed to be far away from g Algebraic geometry is a fascinating branch of mathematics that combines methods from both, algebra and geometry.

Moreover, Grothendieck's schemes invented in the late s allowed the application of algebraic-geometric methods in fields that formerly seemed to be far away from geometry, like algebraic number theory. The new techniques paved the way to spectacular progress such as the proof of Fermat's Last Theorem by Wiles and Taylor. The scheme-theoretic approach to algebraic geometry is explained for non-experts. More advanced readers can use the book to broaden their view on the subject. A separate part deals with the necessary prerequisites from commutative algebra.

On a whole, the book provides a very accessible and self-contained introduction to algebraic geometry, up to a quite advanced level. Every chapter of the book is preceded by a motivating introduction with an informal discussion of the contents.

Typical examples and an abundance of exercises illustrate each section. This way the book is an excellent solution for learning by yourself or for complementing knowledge that is already present. It can equally be used as a convenient source for courses and seminars or as supplemental literature.

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Lists with This Book. This book is not yet featured on Listopia. Community Reviews. Showing Rating details. More filters. Sort order. Start your review of Algebraic Geometry and Commutative Algebra. Jun 29, George rated it it was amazing Shelves: mathematics. The book is divided into two sections. The first half is devoted to commutative algebra, which prepares the reader well for the second half, devoted entirely to scheme theory.

At the start of every new chapter, there are a few pages of introduction to the ideas that will be expanded upon, and to provide a rough, but intuitive, way of thinking of the objects in question and their use. I often get more out of these introductions by reading them back again after I'm done with the chapter. I will start off by what I didn't like. However, despite these drawbacks, you might see I still granted it 5 stars. My reasoning is that the author might not have set out for a concrete understanding through examples, but instead a concrete understanding through a thorough, crystal clear, and systematic exposition of the theory.

And in that, he absolutely excels. The general style of the book is that of giving an abstract but very clear and systematic exposition. By the latter, I mean that the author is very efficient in getting to what he wants to show us; at no point does one feel lost, and on a second reading of a section or chapter, one understands perfectly well why the progression is as it is.

The proofs are also quite easy to follow. Very few times have I been puzzled so as to ask myself 'where did this come from? This is precisely because the author makes the effort to show every explicit detail, even the tedious steps that a less charitable author might have left to the reader; I could count on one hand the amount of times anything is left as an exercise and still have fingers remaining.

In this sense, the book is very complete, since you are left with essentially no possible holes in your understanding that might come up from incomplete proofs or hand-wavy arguments. Indeed, one can show this by First, the commutative algebra part. They both follow a very similar structure in fact, the discussion of primary ideals is almost statement through statement the same , however, the previous paragraph might convince you as to why this book is slightly better than the classic.

Now, the scheme theory part. These are usually considered the basics that any one doing algebraic geometry should know. The structure and ordering of the chapters is quite different to Hartshorne however, as Bosch interplays the scheme theory and the cohomology. Bosch also opts discussing Proj in the final chapter, which makes it so that the reader already has enough confidence with Spec that this will not be too much of a hassle to 'relearn', and indeed much less confusing than a book that discusses Proj right after Spec, since one would have to juggle both objects for the first time simultaneously.

I see myself turning back to this book time and time again when I read a confusing or unclear passage in some other book dealing with similar material. Nitin Rughoonauth added it Nov 11, Ronald Lett marked it as to-read Mar 20, Liam marked it as to-read Jun 11, Martin Berger is currently reading it Apr 16, There are no discussion topics on this book yet. About Siegfried Bosch.

Siegfried Bosch. Books by Siegfried Bosch. Fall in Love with These June Romances. Some people love books. Some people fall in love. And some people fall in love with books about falling in love. Every month our team sorts throug Read more Trivia About Algebraic Geometr No trivia or quizzes yet. Welcome back. Just a moment while we sign you in to your Goodreads account.

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## Algebraic Geometry and Commutative Algebra

Algebraic geometry is a fascinating branch of mathematics that combines methods from both, algebra and geometry. It transcends the limited scope of pure algebra by means of geometric construction principles. The scheme-theoretic approach to algebraic geometry is explained for non-experts. More advanced readers can use the book to broaden their view on the subject. A separate part deals with the necessary prerequisites from commutative algebra. On a whole, the book provides a very accessible and self-contained introduction to algebraic geometry, up to a quite advanced level. Every chapter of the book is preceded by a motivating introduction with an informal discussion of the contents.

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During the last few years we have witnessed a steady flow of books on algebraic geometry, at all levels from advanced monographs to introductory textbooks. Styles range from from classically motivated with plenty of pictures and diagrams to more sober, no need to draw pictures, just commutative diagrams and straight to the core of the subject, sheaves, schemes and cohomology. Well, algebraic geometry deserves all these approaches and more. Someone once wrote that having taught algebraic geometry many times, every time seemed like a new beginning, and with a high probability of no repetition! The book under review takes as its main goal to build the foundations upon which an interested reader can move to more advanced topics, and at the same time keeping the book almost self-contained. Hence, the book is naturally partitioned in two halves. The first part covers the basics of commutative algebra as a prerequisite for the second part, devoted to the category of schemes.