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arXiv · 1407.2745

Extending obstructions to noncommutative functorial spectra

Benno van den Berg·Chris Heunen
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Abstract

Any functor from the category of C*-algebras to the category of locales that assigns to each commutative C*-algebra its Gelfand spectrum must be trivial on algebras of nxn-matrices for n at least 3. This obstruction also applies to other spectra such as those named after Zariski, Stone, and Pierce. We extend these no-go results to functors with values in (ringed) topological spaces, (ringed) toposes, schemes, and quantales. The possibility of spectra in other categories is discussed.

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Benno van den Berg, Chris Heunen. 2014-07-10. Extending obstructions to noncommutative functorial spectra. https://arxiv.org/abs/1407.2745

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