Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 10, Number 3 (2010), 1521-1563.
Spectra, spectra, spectra – Tensor triangular spectra versus Zariski spectra of endomorphism rings
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 –theory and stable –homotopy theory.
Algebr. Geom. Topol., Volume 10, Number 3 (2010), 1521-1563.
Received: 28 May 2009
Revised: 26 March 2010
Accepted: 28 May 2010
First available in Project Euclid: 19 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 18E30: Derived categories, triangulated categories
Secondary: 14F05: Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20] 19K35: Kasparov theory ($KK$-theory) [See also 58J22] 20C20: Modular representations and characters 55P42: Stable homotopy theory, spectra 55U35: Abstract and axiomatic homotopy theory
Balmer, Paul. Spectra, spectra, spectra – Tensor triangular spectra versus Zariski spectra of endomorphism rings. Algebr. Geom. Topol. 10 (2010), no. 3, 1521--1563. doi:10.2140/agt.2010.10.1521. https://projecteuclid.org/euclid.agt/1513715144