Memoirs of the American Mathematical Society 2011; 157 pp; softcover Volume: 210 ISBN10: 082185240X ISBN13: 9780821852408 List Price: US$77 Individual Members: US$46.20 Institutional Members: US$61.60 Order Code: MEMO/210/990
 The author develops a nonabelian 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  Introduction
 Review of some homotopical algebra
 Review of the convergent topos
 Simplicial presheaves associated to isocrystals
 Simplicial presheaves associated to smooth sheaves
 The comparison theorem
 Proofs of 1.71.13
 A base point free version
 Tangential base points
 A generalization
 Appendix A. Exactification
 Appendix B. Remarks on localization in model categories
 Appendix C. The coherator for algebraic stacks
 Appendix D. \(\widetilde B_{\mathrm{cris}}(V)\)admissible implies crystalline
 Bibliography
