Overview

This is an introduction to some geometrie aspects of G-function theory. Most of the results presented here appear in print for the flrst time; hence this text is something intermediate between a standard monograph and a research artic1e; it is not a complete survey of the topic. Except for geometrie chapters (I.3.3, II, IX, X), I have tried to keep it reasonably self- contained; for instance, the second part may be used as an introduction to p-adic analysis, starting from a few basic facts wh ich are recalled in IV.l.l. I have inc1uded about forty exercises, most of them giving some complements to the main text. Acknowledgements This book was written during a stay at the Max-Planck-Institut in Bonn. I should like here to express my special gratitude to this institute and its director, F. Hirzebruch, for their generous hospitality. G. W�stholz has suggested the whole project and made its realization possible, and this book would not exist without his help; I thank him heartily. I also thank D. Bertrand, E. Bombieri, K. Diederich, and S. Lang for their encouragements, and D. Bertrand, G. Christo I and H Esnault for stimulating conversations and their help in removing some inaccuracies after a careful reading of parts of the text (any remaining error is however my sole responsibility).

Full Product Details

Author:   Yves André
Publisher:   Springer Fachmedien Wiesbaden
Imprint:   Vieweg+Teubner Verlag
Edition:   1989 ed.
Volume:   E 13
Dimensions:   Width: 15.50cm , Height: 1.30cm , Length: 23.50cm
Weight:   0.385kg
ISBN:  

9783528063177

ISBN 10:   3528063173
Pages:   232
Publication Date:   01 January 1989
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Language:   German

Table of Contents

One: What are G-functions?.- I: G-functions.- II: Geometric differential equations.- Two: G-functions and differential equations.- III: Fuchsian differential systems: formal theory.- IV: Fuchsian differential systems: arithmetic theory.- V: Local methods.- VI: Global methods.- Three: Diophantine questions.- VII: Independence of values of G-functions.- VIII: A criterium of rationality.- Four: G-functions in arithmetic algebraic geometry.- IX: Towards Grothendieck’s conjecture on periods of algebraic manifolds.- X: Endomorphisms in the fibers of an Abelian pencil.- Glossary of notations.

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