Translator Disclaimer
2010 Spectra, spectra, spectra – Tensor triangular spectra versus Zariski spectra of endomorphism rings
Paul Balmer
Algebr. Geom. Topol. 10(3): 1521-1563 (2010). 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 . We also give a first discussion of the spectrum in two new examples, namely equivariant KK–theory and stable A1–homotopy theory.

Citation

Download Citation

Paul Balmer. "Spectra, spectra, spectra – Tensor triangular spectra versus Zariski spectra of endomorphism rings." Algebr. Geom. Topol. 10 (3) 1521 - 1563, 2010. https://doi.org/10.2140/agt.2010.10.1521

Information

Received: 28 May 2009; Revised: 26 March 2010; Accepted: 28 May 2010; Published: 2010
First available in Project Euclid: 19 December 2017

zbMATH: 1204.18005
MathSciNet: MR2661535
Digital Object Identifier: 10.2140/agt.2010.10.1521

Subjects:
Primary: 18E30
Secondary: 14F05, 19K35, 20C20, 55P42, 55U35

Rights: Copyright © 2010 Mathematical Sciences Publishers

JOURNAL ARTICLE
43 PAGES


SHARE
Vol.10 • No. 3 • 2010
MSP
Back to Top