Contents

pp v-xiii

Preface

pp xiv-xix

Acknowledgments

pp xx-xx

0 - Introductory remarks

pp 1-10

Part I - Tools of p-adic Analysis

pp 11-12

1 - Norms on algebraic structures

pp 13-35

2 - Newton polygons

pp 36-45

3 - Ramification theory

pp 46-55

4 - Matrix analysis

pp 56-76

Part II - Differential Algebra

pp 77-78

5 - Formalism of differential algebra

pp 79-96

6 - Metric properties of differential modules

pp 97-122

7 - Regular and irregular singularities

pp 123-140

Part III - p-adic Differential Equations on Discs and Annuli

pp 141-142

8 - Rings of functions on discs and annuli

pp 143-160

9 - Radius and generic radius of convergence

pp 161-178

10 - Frobenius pullback and pushforward

pp 179-195

11 - Variation of generic and subsidiary radii

pp 196-213

12 - Decomposition by subsidiary radii

pp 214-232

13 - p-adic exponents

pp 233-258

Part IV - Difference Algebra and Frobenius Modules

pp 259-260

14 - Formalism of difference algebra

pp 261-280

15 - Frobenius modules

pp 281-293

16 - Frobenius modules over the Robba ring

pp 294-308

Part V - Frobenius Structures

pp 309-310

17 - Frobenius structures on differential modules

pp 311-322

18 - Effective convergence bounds

pp 323-337

19 - Galois representations and differential modules

pp 338-350

Part VI - The p-adic local monodromy theorem

pp 351-352