Crystalline cohomology

• General Introduction

  See also Sheaf cohomology, Weil cohomology

  <]]>

• Search results

  MathSciNet

  Google Scholar

  Google

  arXiv: Experimental full text search

  arXiv: Abstract search

  <]]>

• Online References

  Note: When starting looking at p-adic cohomology, there are various surveys/introductions by Illusie and Kedlaya to look at.

  Wikipedia

  A proof of the Crystalline conjecture: Niziol

  A survey by Niziol on "p-adic motivic cohomology".

  Bloch: Crystals and de Rham-Witt connections: MR2074428

  MR0565469 review for cryst cohomology intro.

  http://mathoverflow.net/questions/56753/learning-crystalline-cohomology

  http://mathoverflow.net/questions/11648/current-status-of-crystalline-cohomology

  <]]>

• Paper References

  Illusie: Complexe de de Rham-Witt et cohomologie cristalline

  Berthelot: LNM407

  Survey by Illusie in Motives volumes.

  Gillet and Messing: Cycle classes and Riemann-Roch for crystalline cohomology

  Crystalline cohomology of algebraic stacks and Hyodo-Kato cohomology . Asterisque 316.

  <]]>

• Definition

  <]]>

• Properties

  http://mathoverflow.net/questions/68500/poincare-duality-for-crystalline-cohomology

  <]]>

• Standard theorems

  http://math.columbia.edu/~dejong/wordpress/?p=2227 Stacks project on finiteness and comparison with de Rham cohomology.

  <]]>

• Open Problems

  <]]>

• Connections to Number Theory

  <]]>

• Computations and Examples

  http://mathoverflow.net/questions/20381/crystalline-cohomology-of-abelian-varieties

  <]]>

• History and Applications

  <]]>

• Some Research Articles

  Bhatt and de Jong article on comparison with de Rham cohomology: http://front.math.ucdavis.edu/1110.5001

  Bloch: Algebraic K-theory and crystalline cohomology

  Feigin, B.L., Tsygan, B.L.: Additive K-theory and crystalline cohomology. Funktsional. Anal. i Prilozhen. 19, 52–62 (1985)

  Atsushi Shiho, Crystalline fundamental groups and $p$-adic Hodge theory (381--398);

  Mokrane: Cohomologie cristalline des varietes ouvertes (1993)

  Yamasita: p-adic étale cohomology and crystalline cohomology of open varieties

  arXiv:1205.1597 Torsion in the crystalline cohomology of singular varieties from arXiv Front: math.AG by Bhargav Bhatt This note discusses some examples showing that the crystalline cohomology of even very mildly singular projective varieties tends to be quite large. In particular, any singular projective variety with at worst ordinary double points has infinitely generated crystalline cohomology in at least two cohomological degrees. These calculations rely critically on comparisons between crystalline and derived de Rham cohomology.

  <]]>

• Other Information

  http://math.columbia.edu/~dejong/wordpress/?p=1908 de Jong on crystalline cohomology

  http://mathoverflow.net/questions/11648/current-status-of-crystalline-cohomology

  <]]>

• Comments Posted

  <]]>

• Comments

  Write a comment

  There are no comments.

• General Introduction
• Search results
• Online References
• Paper References
• Definition
• Properties
• Standard theorems
• Open Problems
• Connections to Number Theory
• Computations and Examples
• History and Applications
• Some Research Articles
• Other Information
• Comments Posted
• Comments