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020 _a9780821808627
040 _cIISER BPR
041 _aENG
082 _a516.35
_bUEN
_223rd
100 _aUeno, Kenji
245 _aAlgebraic geometry 1 :
_bFrom algebraic varieties to schemes
250 _a1st ed.
260 _aRhode Island :
_bAmerican Mathematical Society,
_cc1999.
300 _axix, 154p. :
_bill, pbk. ;
_c20cm
440 _aTranslations of Mathematical Monographs
_vVol. 185
490 _aIwanami Series in Modern Mathematics
520 _aThis 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 introduction of schemes. Today, most algebraic geometers are well-versed in the language of schemes, but many newcomers are still initially hesitant about them. Ueno's book provides an inviting introduction to the theory, which should overcome any such impediment to learning this rich subject. The book begins with a description of the standard theory of algebraic varieties. Then, sheaves are introduced and studied, using as few prerequisites as possible. Once sheaf theory has been well understood, the next step is to see that an affine scheme can be defined in terms of a sheaf over the prime spectrum of a ring. By studying algebraic varieties over a field, Ueno demonstrates how the notion of schemes is necessary in algebraic geometry. This first volume gives a definition of schemes and describes some of their elementary properties. It is then possible, with only a little additional work, to discover their usefulness. Further properties of schemes will be discussed in the second volume. Ueno's book is a self-contained introduction to this important circle of ideas, assuming only a knowledge of basic notions from abstract algebra (such as prime ideals). It is suitable as a text for an introductory course on algebraic geometry. Includes index.
650 _aMathematics
650 _aAlgebraic Geometry
650 _aAlgebraic Varieties
650 _aAlgebraic Schemes
700 _aKato, Goro
_4Transl.
942 _2ddc
_cBK
999 _c3411
_d3411