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Explore Hodge theory for non-Archimedean analytic spaces in this advanced mathematics lecture by Vladimir Berkovich from the Institute for Advanced Study. Delve into the extension of Deligne's Hodge theory to non-Archimedean settings, focusing on K-analytic spaces and their relationship to C-analytification of separated schemes. Examine the functor that maps schemes to their non-Archimedean K-analytifications and learn about the Hodge theory developed for a specific subcategory of K-analytic spaces. Discover how this theory generalizes complex analytic constructions and connects to Deligne's work. Gain insights into the integral cohomology groups and mixed Hodge structures in both Archimedean and non-Archimedean contexts.
