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Towards Non-Abelian \(p\)-adic Hodge Theory in the Good Reduction Case
Martin C. Olsson, University of California, Berkeley, CA
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Memoirs of the American Mathematical Society
2011; 157 pp; softcover
Volume: 210
ISBN-10: 0-8218-5240-X
ISBN-13: 978-0-8218-5240-8
List Price: US$77
Individual Members: US$46.20
Institutional Members: US$61.60
Order Code: MEMO/210/990
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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

  • 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 1.7-1.13
  • 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
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