Spectral spaces and the Hochster construction

Chris Tedd

Frank Adams 1,

Recall that a topological space X is spectral if X is sober, quasi-compact, and has a basis of quasi-compact open sets, and where the quasi-compact open sets of X are closed under finite intersections. An example of a spectral space is the prime spectrum of a commutative ring with the Zariski topology. In fact, for every spectral space X there is a ring R such that X is isomorphic to Spec R. In this talk I will try to illustrate how we going about constructing such a ring R associated to a space X, via various disparate areas of pure mathematics.

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