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008			160816s2016 si |||| o |||| 0|eng
020			_a9789811091247
040			_aCSL _cCSL
041			_2eng _aeng
084			_aB313 Q6 NBHM _qCSL
100	1		_aNoguchi, Junjiro, _eauthor. _9470815
245	1	0	_aAnalytic Function Theory of Several Variables : _bElements of Oka's Coherence
264		1	_aSingapore : _bImprint: Springer, _c2016.
300			_axviii, 397 p. _bill. _c24 cm
520			_aThe purpose of this book is to present the classical analytic function theory of several variables as a standard subject in a course of mathematics after learning the elementary materials (sets, general topology, algebra, one complex variable). This includes the essential parts of Grauert-Remmert's two volumes, GL227(236) (Theory of Stein spaces) and GL265 (Coherent analytic sheaves) with a lowering of the level for novice graduate students (here, Grauert's direct image theorem is limited to the case of finite maps). The core of the theory is "Oka's Coherence", found and proved by Kiyoshi Oka. It is indispensable, not only in the study of complex analysis and complex geometry, but also in a large area of modern mathematics. In this book, just after an introductory chapter on holomorphic functions (Chap. 1), we prove Oka's First Coherence Theorem for holomorphic functions in Chap. 2. This defines a unique character of the book compared with other books on this subject, in which the notion of coherence appears much later. The present book, consisting of nine chapters, gives complete treatments of the following items: Coherence of sheaves of holomorphic functions (Chap. 2); Oka-Cartan's Fundamental Theorem (Chap. 4); Coherence of ideal sheaves of complex analytic subsets (Chap. 6); Coherence of the normalization sheaves of complex spaces (Chap. 6); Grauert's Finiteness Theorem (Chaps. 7, 8); Oka's Theorem for Riemann domains (Chap. 8). The theories of sheaf cohomology and domains of holomorphy are also presented (Chaps. 3, 5). Chapter 6 deals with the theory of complex analytic subsets. Chapter 8 is devoted to the applications of formerly obtained results, proving Cartan-Serre's Theorem and Kodaira's Embedding Theorem. In Chap. 9, we discuss the historical development of "Coherence". It is difficult to find a book at this level that treats all of the above subjects in a completely self-contained manner. In the present volume, a number of classical proofs are improved and simplified, so that the contents are easily accessible for beginning graduate students.
650		0	_aGeometry, Algebraic. _9812345
650		0	_aCategory theory (Mathematics). _9812370
650		0	_aFunctions of complex variables. _9812172
650		0	_aHomological algebra. _9812371
650	1	4	_aSeveral Complex Variables and Analytic Spaces. _9812372
650	2	4	_aAlgebraic Geometry. _9409661
650	2	4	_aCategory Theory, Homological Algebra. _9812373
942			_2CC _n0 _cTEXL _h B313 Q6 NBHM
999			_c1431553 _d1431553