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A simple proof for Hochster's Theorem
[Submitted on 18 Jun 2026] · 2026-06-19 · via math updates on arXiv.org

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Abstract:We give a conceptual proof for Hochster's Theorem, which asserts that each spectral space is homeomorphic to the spectrum of a ring. Given a ground field and a spectral space, our ring is constructed as filtered direct limit of prime-finite ring, which are attached in a functorial way to finite Kolmogoroff spaces. The construction simplifies an argument of Ershov along these lines. Our crucial ingredient is an assembly of finite Kolmogoroff spaces in terms of coequalizers and pushouts of one-dimensional spaces, and Schwede's observation on prime ideals in cartesian squares of rings.

Submission history

From: Stefan Schröer [view email]
[v1] Thu, 18 Jun 2026 09:47:57 UTC (17 KB)

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