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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Dieudonné rings associated with $ K(n)_\ast \underline{k(n)}_{ \ast}$


Author: Rui Miguel Saramago
Journal: Proc. Amer. Math. Soc. 136 (2008), 2699-2709
MSC (2000): Primary 16W30; Secondary 57T05, 18E10
Published electronically: April 10, 2008
MathSciNet review: 2399031
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Abstract: We use Dieudonné theory for periodically graded Hopf rings to determine the Dieudonné ring structure of the $ \mathbb{Z}/2(p^n - 1)$-graded Morava $ K$-theory $ \overline{K(n)}_\ast (-)$, with $ p$ an odd prime, when applied to the $ \Omega$-spectrum $ \underline{k(n)}_{ \ast}$ (and to $ \underline{K(n)}_{ \ast}$). We also expand these results in order to accomodate the case of the full Morava $ K$-theory $ K(n)_\ast (-)$.


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Additional Information

Rui Miguel Saramago
Affiliation: Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
Email: saramago@math.ist.utl.pt

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09235-6
PII: S 0002-9939(08)09235-6
Keywords: Hopf algebras, Hopf rings, Dieudonn\'e modules, homotopy theory
Received by editor(s): May 22, 2007
Published electronically: April 10, 2008
Additional Notes: The author was partially supported by the Fundação para a Ciência e a Tecnologia through the Program POCI 2010/FEDER
Communicated by: Paul Goerss
Article copyright: © Copyright 2008 American Mathematical Society