**Memoirs of the American Mathematical Society**

2011;
157 pp;
Softcover

MSC: Primary 14;
Secondary 11

Print ISBN: 978-0-8218-5240-8

Product Code: MEMO/210/990

List Price: $81.00

Individual Member Price: $48.60

**Electronic ISBN: 978-1-4704-0607-3
Product Code: MEMO/210/990.E**

List Price: $81.00

Individual Member Price: $48.60

# Towards Non-Abelian \(p\)-adic Hodge Theory in the Good Reduction Case

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*Martin C. Olsson*

The author develops a non–abelian version of \(p\)–adic Hodge Theory for varieties (possibly open with “nice compactification”) with good reduction. This theory yields in particular a comparison between smooth \(p\)–adic sheaves and \(F\)–isocrystals on the level of certain Tannakian categories, \(p\)–adic Hodge theory for relative Malcev completions of fundamental groups and their Lie algebras, and gives information about the action of Galois on fundamental groups.

#### Table of Contents

# Table of Contents

## Towards Non-Abelian $p$-adic Hodge Theory in the Good Reduction Case

- Chapter 1. Introduction 18 free
- Chapter 2. Review of some homotopical algebra 916 free
- Chapter 3. Review of the convergent topos 1926
- Chapter 4. Simplicial presheaves associated to isocrystals 2936
- Chapter 5. Simplicial presheaves associated to smooth sheaves 4754
- Chapter 6. The comparison theorem 6370
- Chapter 7. Proofs of 1.7--1.13 7380
- Chapter 8. A base point free version 8592
- Chapter 9. Tangential base points 97104
- Chapter 10. A generalization 123130
- Appendix A. Exactification 125132
- Appendix B. Remarks on localization in model categories 135142
- Appendix C. The coherator for algebraic stacks 139146
- Appendix D. B"0365Bcris(V)-admissible implies crystalline. 147154
- Bibliography 155162