• Tags
  • #arithmetic-geometry #arithmetic-geometry/p-adic-hodge-theory
• Refs:
  • https://math.stanford.edu/~conrad/papers/notes.pdf
  • Course notes: https://www.dropbox.com/s/2gua6n5r0spx8i5/p-adicHodge.pdf?dl=0 #resources/course-notes
  • A survey of comparison theorems and period rings: https://arxiv.org/pdf/2005.07919.pdf#page=1 #resources/summaries A nice summary #resources/summaries
  • 2020 UMich course: http://www-personal.umich.edu/~ahorawa/math_679_p-adic_Hodge.pdf#page=2
• Links:
  • Hodge theory MOC
  • kahler
  • etale cohomology
  • cyclotomic character
  • Hodge-Tate decomposition
  • Main theorems:
    • Hodge-Tate conjecture
    • de Rham conjecture
    • crystalline conjecture
    • semistable conjecture
    • potentially semistable conjecture
  • syntomic
  • period ring
  • alteration
  • Hodge F-crystal
  • The many cohomology theories:
    • etale cohomology
    • l-adic cohomology
    • de Rham cohomology
    • Hodge-Tate cohomology
    • crystalline cohomology
    • de Rham-Witt

p-adic Hodge theory

Notation

Motivations and Ideas

One of the best-known tools for studying Galois representations of the absolute Galois group of \({\mathbf{Q}}\).

Main theorems

Motivations

See period rings.

Main theorems

Notes

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On the importance of tilting Pasted image 20211106012609.png

Applications

To Galois cohomology: