Lectures on Analytic Geometry
        Peter Scholze (all results joint with Dustin Clausen)
                                                                Contents
                Analytic Geometry                                                                                            5
                   Preface                                                                                                   5
                   1.  Lecture I: Introduction                                                                               6
                   2.  Lecture II: Solid modules                                                                            11
                   3.  Lecture III: Condensed R-vector spaces                                                               16
                   4.  Lecture IV: M-complete condensed R-vector spaces                                                     20
                   Appendix to Lecture IV: Quasiseparated condensed sets                                                    26
                   5.  Lecture V: Entropy and a real B+                                                                     28
                                                            dR
                   6.  Lecture VI: Statement of main result                                                                 33
                   Appendix to Lecture VI: Recollections on analytic rings                                                  39
                   7.  Lecture VII: Z((T))       is a principal ideal domain                                                42
                                              >r
                   8.  Lecture VIII: Reduction to “Banach spaces”                                                           47
                   Appendix to Lecture VIII: Completions of normed abelian groups                                           54
                   Appendix to Lecture VIII: Derived inverse limits                                                         56
                   9.  Lecture IX: End of proof                                                                             57
                   Appendix to Lecture IX: Some normed homological algebra                                                  65
                   10.   Lecture X: Some computations with liquid modules                                                   69
                   11.   Lecture XI: Towards localization                                                                   73
                   12.   Lecture XII: Localizations                                                                         79
                   Appendix to Lecture XII: Topological invariance of analytic ring structures                              86
                   Appendix to Lecture XII: Frobenius                                                                       89
                   Appendix to Lecture XII: Normalizations of analytic animated rings                                       93
                   13.   Lecture XIII: Analytic spaces                                                                      95
                   14.   Lecture XIV: Varia                                                                                103
                Bibliography                                                                                               109
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