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＜電子ブック＞
Nevanlinna Theory in Several Complex Variables and Diophantine Approximation / by Junjiro Noguchi, Jörg Winkelmann
(Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics. ISSN:21969701 ; 350)

版	1st ed. 2014.
出版者	(Tokyo : Springer Japan : Imprint: Springer)
出版年	2014
本文言語	英語
大きさ	XIV, 416 p. 6 illus : online resource
著者標目	*Noguchi, Junjiro author Winkelmann, Jörg author SpringerLink (Online service)
件　名	LCSH:Functions of complex variables LCSH:Algebraic geometry LCSH:Number theory FREE:Functions of a Complex Variable FREE:Several Complex Variables and Analytic Spaces FREE:Algebraic Geometry FREE:Number Theory
一般注記	Nevanlinna Theory of Meromorphic Functions -- First Main Theorem -- Differentiably Non-Degenerate Meromorphic Maps -- Entire Curves into Algebraic Varieties -- Semi-Abelian Varieties -- Entire Curves into Semi-Abelian Varieties -- Kobayashi Hyperbolicity -- Nevanlinna Theory over Function Fields -- Diophantine Approximation -- Bibliography -- Index -- Symbols The aim of this book is to provide a comprehensive account of higher dimensional Nevanlinna theory and its relations with Diophantine approximation theory for graduate students and interested researchers. This book with nine chapters systematically describes Nevanlinna theory of meromorphic maps between algebraic varieties or complex spaces, building up from the classical theory of meromorphic functions on the complex plane with full proofs in Chap. 1 to the current state of research. Chapter 2 presents the First Main Theorem for coherent ideal sheaves in a very general form. With the preparation of plurisubharmonic functions, how the theory to be generalized in a higher dimension is described. In Chap. 3 the Second Main Theorem for differentiably non-degenerate meromorphic maps by Griffiths and others is proved as a prototype of higher dimensional Nevanlinna theory. Establishing such a Second Main Theorem for entire curves in general complex algebraic varieties isa wide-open problem. In Chap. 4, the Cartan-Nochka Second Main Theorem in the linear projective case and the Logarithmic Bloch-Ochiai Theorem in the case of general algebraic varieties are proved. Then the theory of entire curves in semi-abelian varieties, including the Second Main Theorem of Noguchi-Winkelmann-Yamanoi, is dealt with in full details in Chap. 6. For that purpose Chap. 5 is devoted to the notion of semi-abelian varieties. The result leads to a number of applications. With these results, the Kobayashi hyperbolicity problems are discussed in Chap. 7. In the last two chapters Diophantine approximation theory is dealt with from the viewpoint of higher dimensional Nevanlinna theory, and the Lang-Vojta conjecture is confirmed in some cases. In Chap. 8 the theory over function fields is discussed. Finally, in Chap. 9, the theorems of Roth, Schmidt, Faltings, and Vojta over number fields are presented and formulated in view of Nevanlinna theory with results motivated by those in Chaps. 4, 6, and 7 HTTP:URL=https://doi.org/10.1007/978-4-431-54571-2

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