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arXiv · 2205.09863

Non-Archimedean Fr\'echet Algebras and the Loop Space of a Hypersurface Complement

Emile Bouaziz
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Abstract

We study the space of loops into a hypersurface complement, and show that the corresponding topological algebra of Laurent series with coefficients in $\mathcal{O}(L\mathbf{A}^{d}_{f})$ is a topological localisation of $\mathcal{O}(L\mathbf{A}^{d})$. This requires introducing a small amount of non-Archimedean functional analysis. In particular we work with topological algebras whose topology is generated by a family of sub-multiplicative, non-Archimedean semi-norms.

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Emile Bouaziz. 2022-05-19. Non-Archimedean Fr\'echet Algebras and the Loop Space of a Hypersurface Complement. https://arxiv.org/abs/2205.09863

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