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020			_a9780821813577
040			_cIISER BPR
041			_aENG
082			_a516.35 _bUEN _223rd
100			_aUeno, Kenji
245			_aAlgebraic geometry 2 : _bSheaves and cohomology
250			_a1st ed.
260			_aRhode Island : _bAmerican Mathematical Society, _cc2001.
300			_av, 184p. : _bill, pbk. ; _c20cm.
440			_aTranslations of Mathematical Monographs ; _vVol. 197
490			_aIwanami Series in Modern Mathematics
520			_aModern algebraic geometry is built upon two fundamental notions: schemes and sheaves. The theory of schemes was explained in Algebraic Geometry 1: From Algebraic Varieties to Schemes, (see Volume 185 in the same series, Translations of Mathematical Monographs). In the present book, Ueno turns to the theory of sheaves and their cohomology. Loosely speaking, a sheaf is a way of keeping track of local information defined on a topological space, such as the local holomorphic functions on a complex manifold or the local sections of a vector bundle. To study schemes, it is useful to study the sheaves defined on them, especially the coherent and quasicoherent sheaves. The primary tool in understanding sheaves is cohomology. For example, in studying ampleness, it is frequently useful to translate a property of sheaves into a statement about its cohomology. The text covers the important topics of sheaf theory, including types of sheaves and the fundamental operations on them, such as ... coherent and quasicoherent sheaves. proper and projective morphisms. direct and inverse images. Cech cohomology. For the mathematician unfamiliar with the language of schemes and sheaves, algebraic geometry can seem distant. However, Ueno makes the topic seem natural through his concise style and his insightful explanations. He explains why things are done this way and supplements his explanations with illuminating examples. As a result, he is able to make algebraic geometry very accessible to a wide audience of non-specialists. Includes index.
650			_aMathematics
650			_aAlgebraic Geometry
650			_aSheaves and Cohomology
700			_aKato, Goro _4Transl.
942			_2ddc _cBK
999			_c3410 _d3410