Algebraic Geometry: From Algebraic Varieties to Schemes
This is the first of three volumes on algebraic geometry. The second volume, Algebraic Geometry 2: Sheaves and Cohomology, is available from the AMS as Volume 197 in the Translations of Mathematical Monographs series. Early in the 20th century, algebraic geometry underwent a significant overhaul, as mathematicians, notably Zariski, introduced a much stronger emphasis on algebra and rigor into the subject. This was followed by another fundamental change in the 1960s with Grothendieck's...
Search in google:
PrefacePreface to the English TranslationSummary and GoalsCh. 1Algebraic Varieties11.1Algebraic Sets11.2Hilbert's Nullstellensatz61.3Affine Algebraic Varieties121.4Multiplicity and Local Intersection Multiplicity261.5Projective Varieties291.6What is Missing?38Ch. 2Schemes432.1Prime Spectrum432.2Affine Schemes512.3Ringed Space and Scheme752.4Schemes and Morphisms88Ch. 3Categories and Schemes1013.1Categories and Functors1013.2Representable Functors and Fibre Products1153.3Separated Morphisms131Solutions to Problems139Solutions to Exercises147Index153
\ BooknewsDevelops Grothendieck's scheme theory as a method for studying algebraic geometry. Ueno sets forth the definition and main properties of schemes, together with necessary material from the theory of algebraic varieties and category theory. Originally published in Japanese by Iwanami Shoten, Tokyo in 1997. Annotation c. Book News, Inc., Portland, OR (booknews.com)\ \
