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Anke Pietsch

Tea Seminar: Sruthy Joseph (University of Muenster): Condensed abelian groups and duality

Tuesday, 03.06.2025 14:15 im Raum M3

Mathematik und Informatik

Condensed mathematics was developed by Dustin Clausen and Peter Scholze to address difficulties in doing algebra on algebraic structures that carry a topology. For instance, we cannot do homological algebra in the category of topological abelian groups because it does not form an abelian category. This necessity has given rise to the category of condensed abelian groups, which forms an abelian category. In the first half of the talk, I am reformulating the definition of condensed sets in the language of Boolean rings using Stone duality. The second half focuses on discussing the properties of the category of condensed abelian groups. I also propose a candidate for the Pontryagin dual of a condensed abelian group and demonstrate why this choice of dual does not satisfy Pontryagin duality in the category of condensed abelian groups.



Angelegt am 27.05.2025 von Anke Pietsch
Geändert am 27.05.2025 von Anke Pietsch
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