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Condensed Shape of a Scheme

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Catrin Mair
TU Darmstadt
Mon, 19/06/2023 - 15:00 - 16:00
MPIM Lecture Hall

The $\infty$-category Cond(Ani) of condensed anima combines homotopy theory with the topological space direction of condensed sets. For example, we can recover the "Shape" of a sufficiently nice topological space from the corresponding condensed anima. In my talk, I will focus on explaining how to define a refinement of the étale homotopy type of a scheme as an object in Cond(Ani) following constructions from Shape Theory. This condensed version of a homotopy type, which I will refer to as condensed shape, is closely related to the pro-étale topology and the work of Barwick, Glasman and Haine in the Exodromy paper.


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