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De Rham cohomology: from smooth algebraic varieties to dagger geometry

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If you have a question about this talk, please contact Alexis Marchand .

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In this talk, I will begin by reviewing the definition of algebraic de Rham cohomology, for a smooth complex algebraic variety X, and recalling a well-known result of Grothendieck which relates this cohomology to the singular cohomology of the analytification of X. One of the shortcomings of Tate’s model of non-archimedean geometry is that the algebraic approach to de Rham cohomology does not generalise to give a satisfactory theory in this setting. In the remainder of my talk, I will explain why this is the case and, if there is time, illustrate how Grosse-Klonne fixed this problem through the introduction of dagger spaces.

This talk is part of the Junior Geometry Seminar series.

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