Volume 10, issue 3 (2010)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Spectra, spectra, spectra – Tensor triangular spectra versus Zariski spectra of endomorphism rings

Paul Balmer

Algebraic & Geometric Topology 10 (2010) 1521–1563
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 . 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 2000
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
Paul Balmer
Mathematics Department
UCLA
Box 951555
Los Angeles 90095-1555
United States
http://www.math.ucla.edu/~balmer