The Historical Development of Algebraic Geometry

This is an enriched transcription of footage posted by the University of Wisconsin–Milwaukee Department of Mathematical Sciences [1]. The images are composites of screenshots from the footage manipulated with Python and the Python OpenCV library [2]. These materials were prepared by Ryan C. Schwiebert with the goal of capturing and restoring some of the material. The lecture presents the content of Dieudonné’s article of the same title [3] as well as the content of earlier lecture notes [4], but the live lecture is naturally embellished with different details. The text presented here is, for the most part, written as it was spoken. This is why there are some ungrammatical constructions of spoken word, and some linguistic quirks of a French speaker. The transcriber has taken some liberties by abbreviating places where Dieudonné self-corrected. That is, short phrases which turned out to be false starts have been elided, and now only the subsequent word-choices that replaced them appear. Unfortunately, time has taken its toll on the footage, and it appears that a brief portion at the beginning, as well as the last enumerated period (VII. Sheaves and schemes), have been lost. (Fortunately, we can still read about them in [3]!) The audio and video quality has contributed to several transcription errors. Finally, a lack of thorough knowledge of the history of algebraic geometry has also contributed some errors. Contact with suggestions for improvement of the materials is welcome.