Abstract
We study the topological spectrum of a seminormed ring which we define as the space of prime ideals such that equals the kernel of some bounded power-multiplicative seminorm. For any seminormed ring we show that is a quasicompact sober topological space. When is a perfectoid Tate ring we construct a natural homeomorphism
between the topological spectrum of and the topological spectrum of its tilt . As an application, we prove that a perfectoid Tate ring is an integral domain if and only if its tilt is an integral domain.
Citation
Dimitri Dine. "Topological spectrum and perfectoid Tate rings." Algebra Number Theory 16 (6) 1463 - 1500, 2022. https://doi.org/10.2140/ant.2022.16.1463
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