Table of contents : Narasimhan R.Grauert_s theorem on direct images of coherent sheaves (sem.math.sup.,vol.40)(UNIVE.MONTREAL,1971) 4......Page 4 Copyright 5......Page 5 CONTENTS 6......Page 6 INTRODUCTION 7 ......Page 7 CHAPTER I - Theorem of Cartan on privilege 10 ......Page 10 CHAPTER II - The Grauert norm 18 ......Page 18 CHAPTER III - The theorem on privilege for the Grauert norm 22 ......Page 22 CHAPTER IV - Theorem B with bounds 28 ......Page 28 CHAPTER V - Thickening Stein spaces 35 ......Page 35 CHAPTER VI - Admissible covers 41 ......Page 41 CHAPTER VII - Leray’s theorem with bounds 49 ......Page 49 CHAPTER VIII - The induction process 55 ......Page 55 cover......Page 1