Jacob Lurie: A Riemann-Hilbert Correspondence in P-adic Geometry

Explore the fourth part of Jacob Lurie's lecture series on the Riemann-Hilbert correspondence in p-adic geometry. Delve into advanced mathematical concepts such as perfectoid Riemann-Hilbert functors, perfected Hodge-Tate crystals, and perfectoidization of schemes. Examine the properties of perfectoidization, spectral methods, and the computation of perfectoidization. Investigate the module structure on RH, affineness of perfectoidization, and properties of the Riemann-Hilbert functor in both characteristic p and mixed characteristic settings. Learn about finiteness theorems, globalization, rigid geometry, and Zavyalov's theorem. Conclude with an exploration of the primitive comparison theorem, exactness, duality, and applications of these complex mathematical ideas.