Colin McLarty

Case Western Reserve University

"How Grothendieck Simplified Geometry"

Abstract:

Andre Weil in 1949 made some conjectures in arithmetic. He drew on 19th century ideas (zeta functions) to simplify the statements. He suggested how some then non-existent topological ideas could simplify the proof to the level of graduate exercises in linear algebra. Jean-Pierre Serre, Alexander Grothendieck, and Pierre Deligne pursued those ideas, even as Weil lost faith in them, and discovered them though not entirely in the form anyone had hoped for. There turned out to be two very different senses of simplicity: concise, elegant use of high powered results versus developing perfectly adapted low powered tools.

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