van den Berg, Benno; Heunen, Chris

Extending obstructions to noncommutative functorial spectra

Theory Appl. Categ. 29, 457-474, electronic only (2014)

Summary

Summary: 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 $n$-by-$n$ matrices for $n \geq 3$. 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.

Mathematics Subject Classification

16B50, 46L85

Keywords/Phrases

ring spectra

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