Algebraic families of \(E_\infty\)-spectra
type: Item
instance of: scholarly article
title: Algebraic families of \(E_\infty\)-spectra
zbMATH Open document ID: 0934.55008
DOI: 10.1016/S0166-8641(98)00106-0
author: Paulo Lima-Filho
published in: Topology and its Applications
publication date: 2000-04-13T00:00:00Z
review text: In the paper under review, a spectrum \(S\) is a collection of based spaces \(\{S(n)\mid n\in\mathbb{N}\}\) together with a compatible family of homeomorphisms \(s_n:S(n)\to\Omega S(n+1)\) for all \(n\in\mathbb{N}\). Recall that a spectrum determintes a generalized cohomology theory. The author shows how to associate three distinct spectra to a complex projective variety \(X\): the morphic spectrum (an \(E_\infty\)-ring spectrum), the multiplicative morphic spectra and the holomorphic \(K\)-theory spectrum. All these constructions are contravariantly functorial on \(X\) and they are based on standard infinite loop space machinery. The coefficients of cohomology theories associated to the spectra reflect algebraic geometric and topological invariants for \(X\). In the morphic case the coefficients are given in terms of Friedlander-Lawson's morphic cohomology [\textit{E. M. Friedlander} and \textit{H. B. Lawson} jun., Ann. Math., II. Ser. 136, No.~2, 361-428 (1992; Zbl 0788.14014)]. The reviewer mentions that the author tries to be as self-contained as possible in the area. For example, he introduces in Section 2 of the work, the basic moduli spaces of algebraic cycles and the mapping spaces associated to them, which are the central tool in his constructions.
Mathematics Subject Classification ID: 55P42
Mathematics Subject Classification ID: 55N20
Mathematics Subject Classification ID: 14C25
Mathematics Subject Classification ID: 14C05
Mathematics Subject Classification ID: 14F99
Mathematics Subject Classification ID: 55P43
zbMATH DE Number: 1367564
zbMATH Keywords: spectra
zbMATH Keywords: algebraic cycles
zbMATH Keywords: morphic cohomology
zbMATH Keywords: holomorphic \(K\)-theory
reviewed by: Cristian N. Costinescu
MaRDI profile type: Publication
full work available at URL: s0166-8641(98)00106-0
OpenAlex ID: W2081583422
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description: scientific article; zbMATH DE number 1367564