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Explore advanced concepts in Analytic Geometry through this IAS/PU Arithmetic Geometry lecture focusing on the analytic de Rham stack and its applications in p-adic Hodge theory. Delve into the construction's unique ability to encode p-adic D-modules through quasi-coherent sheaves, even in scenarios lacking differentials such as perfectoid spaces and Fargues-Fontaine curves. Learn how the Fargues-Fontaine de Rham stacks serve as analytic objects whose cohomology theories provide refined versions of traditional de Rham cohomology of rigid spaces, specifically through the Fargues-Fontaine de Rham cohomology of Le Bras-Vezzani. Presented by Juan Esteban Rodriguez Camargo from Columbia University, this technical discussion offers valuable insights into cutting-edge developments in mathematical theory.
