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The periodic Hopf ring of connective Morava K-theory

The periodic Hopf ring of connective Morava K-theory Abstract. Let Knà À denote the n-th periodic Morava K-theory for any ®xed odd prime p. Let kn à denote the -spectrum of the n-th connective Morava K-theory. We compute the Hopf ring Knà kn à . 1991 Mathematics Subject Classi®cation: 55N20. 1. Introduction Let p be any odd prime, ®xed for the duration of this article. Let Kn be the spectrum of the periodic (of period 2 p n À 1) n-th Morava K-theory and let kn be the spectrum of the connective n-th Morava K-theory. Morava K-theory was ®rst de®ned and studied by Jack Morava in numerous unpublished preprints. Both Kn and kn are commutative, associative, ring spectra with unit. The coe½cient rings Kn à and kn à are Fp vn Y vÀ1 and Fp vn , respectively, where the degree jvn j of vn is n 2 p n À 1 and Fp is the p-element ®eld. See [JW75] for an early published account of some of Morava's work. There is a canonical map of ring spectra kn 3 Kn. Recall that Knà X vÀ1 knà X knà X nknà Kn à . The map knà X 3 Knà X induced by the above n http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

The periodic Hopf ring of connective Morava K-theory

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References (7)

Publisher
de Gruyter
Copyright
Copyright (c)1999 by Walter de Gruyter GmbH & Co. KG
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/form.1999.024
Publisher site
See Article on Publisher Site

Abstract

Abstract. Let Knà À denote the n-th periodic Morava K-theory for any ®xed odd prime p. Let kn à denote the -spectrum of the n-th connective Morava K-theory. We compute the Hopf ring Knà kn à . 1991 Mathematics Subject Classi®cation: 55N20. 1. Introduction Let p be any odd prime, ®xed for the duration of this article. Let Kn be the spectrum of the periodic (of period 2 p n À 1) n-th Morava K-theory and let kn be the spectrum of the connective n-th Morava K-theory. Morava K-theory was ®rst de®ned and studied by Jack Morava in numerous unpublished preprints. Both Kn and kn are commutative, associative, ring spectra with unit. The coe½cient rings Kn à and kn à are Fp vn Y vÀ1 and Fp vn , respectively, where the degree jvn j of vn is n 2 p n À 1 and Fp is the p-element ®eld. See [JW75] for an early published account of some of Morava's work. There is a canonical map of ring spectra kn 3 Kn. Recall that Knà X vÀ1 knà X knà X nknà Kn à . The map knà X 3 Knà X induced by the above n

Journal

Forum Mathematicumde Gruyter

Published: Nov 1, 1999

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