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...Lectures on analytic geometry peter scholze all results joint with dustin clausen contents preface lecture i introduction ii solid modules iii condensed r vector spaces iv m complete appendix to quasiseparated sets v entropy and a real b dr vi statement of main result recollections rings vii z t is principal ideal domain viii reduction banach completions normed abelian groups derived inverse limits ix end proof some homological algebra x computations liquid xi towards localization xii localizations topological invariance ring structures frobenius normalizations animated xiii xiv varia bibliography...