Having said that, this is absolutely my (current) favorite introductory textbook on the subject. In the interest of full disclosure, I should note at the outset that I do arithmetic geometry, so the amount of modern algebraic geometry I consider to be foundational is considerable (I've been learning this stuff for over 4 years and there is still a ton that I don't know). Torsten Wedhorn, Department of Mathematics, University of Paderborn Ulrich Görtz, Institute of Experimental Mathematics, University Duisburg-Essen Prof. Prevarieties - Spectrum of a Ring - Schemes - Fiber products - Schemes over fields - Local properties of schemes - Quasi-coherent modules - Representable functors - Separated morphisms - Finiteness Conditions - Vector bundles - Affine and proper morphisms - Projective morphisms - Flat morphisms and dimension - One-dimensional schemes - Examples Prof. It will be complemented by a second volume on the cohomology of schemes. Essential facts from commutative algebra are assembled in an appendix. To get startet, it requires only basic knowledge in abstract algebra and topology. The volume at hand is an introduction to schemes. The text is complemented by many exercises that serve to check the comprehension of the text, treat further examples, or give an outlook on further results. Thus the reader experiences that the further development of the theory yields an ever better understanding of these fascinating objects. Several examples from the realm of Hilbert modular surfaces and of determinantal varieties are used methodically to discuss the covered techniques. A systematic treatment and motivation of the theory is emphasized, using concrete examples to illustrate its usefulness. It presents Grothendieck's technically demanding language of schemes that is the basis of the most important developments in the last fifty years within this area. This book introduces the reader to modern algebraic geometry. To learn more about how and for what purposes Amazon uses personal information (such as Amazon Store order history), please visit our Privacy Notice. You can change your choices at any time by visiting Cookie Preferences, as described in the Cookie Notice. Click ‘Customise Cookies’ to decline these cookies, make more detailed choices, or learn more. Third parties use cookies for their purposes of displaying and measuring personalised ads, generating audience insights, and developing and improving products. This includes using first- and third-party cookies, which store or access standard device information such as a unique identifier. If you agree, we’ll also use cookies to complement your shopping experience across the Amazon stores as described in our Cookie Notice. We also use these cookies to understand how customers use our services (for example, by measuring site visits) so we can make improvements. We use cookies and similar tools that are necessary to enable you to make purchases, to enhance your shopping experiences and to provide our services, as detailed in our Cookie Notice.
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