Algebraic & Geometric Topology 10 (2010) 1521–1563

DOI: 10.2140/agt.2010.10.1521

Abstract

We construct a natural continuous map from the triangular spectrum of a tensor triangulated category to the algebraic Zariski spectrum of the endomorphism ring of its unit object. We also consider graded and twisted versions of this construction. We prove that these maps are quite often surjective but far from injective in general. For instance, the stable homotopy category of finite spectra has a triangular spectrum much bigger than the Zariski spectrum of Z. We also give a first discussion of the spectrum in two new examples, namely equivariant KK–theory and stable A¹–homotopy theory.

Keywords

tensor triangular geometry, spectra

Mathematical Subject Classification

Primary: 18E30

Secondary: 14F05, 19K35, 20C20, 55P42, 55U35

References

Publication

Received: 28 May 2009
Revised: 26 March 2010
Accepted: 28 May 2010
Published: 2 July 2010

Authors