Some p-adic Geometry Notes

Short personal introductory notes on perfectoid spaces, adic spaces, diamonds, and Fargues-Fontaine curves based on the Scholze-Weinstein lecture notes with some annotations, classical analogies, and explicit computations.

Periods (ongoing casual writing)

I am trying to eventually write up a coherent story of p-adic period integrals, period rings, periods as functors, and periods in geometrization.

Section 1 briefly surveys periods in the classical complex setting and the equivalence of a filtration to a modification of a trivial bundle at a boundary point via the Rees construction, central to Simpson's geometrization. Section 2 transitions into the p-adic setting. Later, I am hoping to introduce the D_B functor by pairing and talk about how Galois Tate twists Q_p(n) translate into geometric Serre twists O(n) on the Fargues-Fontaine curve. Section 3 will explore heuristics for global deformations and integral liftability.