G-Functions and Geometry

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).