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- prism
- tilting
- Faltings almost purity
- semistable reduction
- weight monodromy conjecture
- perfect field
- tilting
- solid mathematics
- condensed sets
perfectoid
Idea: the mixed characteristic analogs of Fp-Alg.
Definition: the perfection or perfect closure of a field:
kperf:=⋃n≥1k1pn⊆¯k.
# References
- https://www.youtube.com/watch?v=3YF6fCFbymk&list=PLCe-H2N8-ny5O8svc5I4RAhPFj7AmH9Jq
- Lots of notes from a 2015 learning seminar: https://math.stanford.edu/~conrad/Perfseminar/
Topics
- Perfectoid ring
- smooth algebra
- Formal spectrum
- Crystalline cohomology
- Prismatic cohomology
- What does it mean for an algebra over Qp to be ramified at p?