Towards non-Abelian p-adic Hodge theory in the good reduction case / Martin C. Olsson.

Format:

Book

Author/Creator:

Olsson, Martin C., author.

Series:

Memoirs of the American Mathematical Society ; Volume 210, Number 990.

Memoirs of the American Mathematical Society, 0065-9266 ; Volume 210, Number 990

Language:

English

Subjects (All):

Hodge theory.

p-adic analysis.

Variants.

Physical Description:

1 online resource (157 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2010.

Language Note:

English

Summary:

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.

Contents:

""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Review of some homotopical algebra""; ""Chapter 3. Review of the convergent topos""; ""Chapter 4. Simplicial presheaves associated to isocrystals""; ""Chapter 5. Simplicial presheaves associated to smooth sheaves""; ""Chapter 6. The comparison theorem""; ""Chapter 7. Proofs of 1.7

1.13""; ""Chapter 8. A base point free version""; ""Chapter 9. Tangential base points""; ""Chapter 10. A generalization""; ""Appendix A. Exactification""; ""Appendix B. Remarks on localization in model categories""

""Appendix C. The coherator for algebraic stacks""""Appendix D. B""0365Bcris(V)-admissible implies crystalline.""; ""Bibliography""

Notes:

"Volume 210, Number 990 (end of volume)."

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0607-1