• Tags
  • #arithmetic-geometry/p-adic-hodge-theory\
• References:
  • http://www-personal.umich.edu/~bhattb/teaching/prismatic-columbia/lecture1-overview.pdf #resources/notes
  • http://www-personal.umich.edu/~bhattb/teaching/prismatic-columbia/ #resources/notes
  • Yuri’s giant reading list: https://www.math.brown.edu/ysulyma/reading.html #resources/recommendations
  • Bhatt-Lurie 2022, Absolute Prismatic Cohomology. https://arxiv.org/pdf/2201.06120.pdf#page=1 #resources/papers/2022
• Links:
  • Unsorted/Masterclass in Condensed Mathematics
  • The Nygaard filtration
  • Tate twist
  • perfectoid MOC
  • p-adic Hodge theory
  • spec Z as a curve
  • topological K theory
  • MMP
  • p-adic etale K theory
  • Riemann-Hilbert correspondence

prismatic cohomology

Motivations

A cohomology theory for mixed characteristic rings, inspired by calculations in stable homotopy and Galois representations. Used in the proof of a mixed characteristic analog of Kodaira vanishing, yielding a minimal model program in the birational geometry of arithmetic threefolds. Used in a proof of the Bott vanishing theorem in algebraic K theory.

Motivations from p-adic Hodge theory, THH

Definitions

# Examples

Notes

Syntomic complexes

See Tate twist, motivic cohomology.

Applications