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Claudia Lückert

Wilhelm Killing Kolloquium: Prof. Dr. Katharina Hübner (Goethe Universität Frankfurt): Paths in nonarchimedean spaces

Thursday, 24.04.2025 14:15 im Raum M4

Mathematik und Informatik

If we complete the rational numbers $\mathbb{Q}$ with respect to the standard absolute value, we obtain the reals $\mathbb{R}$, wich is a connected topological space. The completion $\mathbb{Q}_p$ of $\mathbb{Q}$ with respect to the $p$-adic valuation for a prime $p$, however, is totally disconnected. So it seems that the concept of a path connecting two points in the $p$-adic numbers $\mathbb{Q}_p$ (or $\mathbb{Q}_p^n$) does not make sense. In fact, the space $\mathbb{Q}_p$ itself is not quite suitable for doing geometry. Instead one can consider the affine line $\mathbb{A}_{\mathbb{Q}_p}^1$ as an adic space. It contains $\mathbb{Q}_p$ as so called \emph{classical points} but has many more points. In this talk we will convince ourselves that $\mathbb{A}_{\mathbb{Q}_p}^1$ is indeed path connected if we use the right notion of a path.



Angelegt am 17.03.2025 von Claudia Lückert
Geändert am 09.04.2025 von Claudia Lückert
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Kolloquium Wilhelm Killing
Vorträge des SFB 1442