Submission date: 31 August 2023

Abstract:

Extending our insights from [NVOstrowski], we apply point-free techniques to sharpen a foundational result in Berkovich geometry. In our language, given the ring A:=K{R^{-1}T} of convergent power series over a suitable non-Archimedean field K, the points of its Berkovich Spectrum M(A) correspond to R-good filters. The surprise is that, unlike the original result by Berkovich, we do not require the field K to be non-trivially valued. Our investigations into non-Archimedean geometry can be understood as being framed by the question: what is the relationship between topology and logic?

Mathematics Subject Classification: 03G30, 06D22, 14G22

Keywords and phrases:

Full text arXiv 2308.16472: pdf, ps.