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Refs:
- Course notes on p-adic geometry: https://www.dropbox.com/s/j53etb62pfjcp57/sntsnotes.pdf?dl=0 #resources/course-notes
- Lectures by Kedlaya: https://www.youtube.com/watch?v=yyLLemzaCRQ
- Course on adic spaces: http://perso.ens-lyon.fr/sophie.morel/adic_notes.pdf#page=1 #resources/full-courses
- https://www.youtube.com/watch?v=3YF6fCFbymk&list=PLCe-H2N8-ny5O8svc5I4RAhPFj7AmH9Jq #resources/videos
- Lots of notes from a 2015 learning seminar: https://math.stanford.edu/~conrad/Perfseminar/ #resources/websites
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Links:
- prism
- prismatic cohomology
- tilting
- Faltings almost purity
- semistable reduction
- weight monodromy conjecture
- Unsorted/perfect field
- Unsorted/tilting
- solid mathematics
- condensed sets
- affine Grassmannian
- Huber ring
- Perfectoid ring
- Unsorted/smooth algebra
- Formal spectrum
- Crystalline cohomology
- Prismatic cohomology
- What does it mean for an algebra over \({ {\mathbf{Q}}_p }\) to be ramified at \(p\)?
perfectoid
Idea: the mixed characteristic analogs of \({ {}_{{ \mathbf{F} }_p} \mathsf{Alg} }\).
Definition: the perfection or perfect closure of a field:
\begin{align*}
k^{\mathrm{perf}}\coloneqq\bigcup_{n\geq 1} k^{1\over p^n} \subseteq \mkern 1.5mu\overline{\mkern-1.5muk\mkern-1.5mu}\mkern 1.5mu
.\end{align*}
Recent result: used by Yves André to prove Hochster's Direct Summand Conjecture. # Perfection
References
Examples
