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2007 Dieudonné modules and $p$–divisible groups associated with Morava $K$–theory of Eilenberg–Mac Lane spaces
Victor M Buchstaber, Andrey Lazarev
Algebr. Geom. Topol. 7(2): 529-564 (2007). DOI: 10.2140/agt.2007.7.529


We study the structure of the formal groups associated to the Morava K–theories of integral Eilenberg–Mac Lane spaces. The main result is that every formal group in the collection {K(n)K(,q),q=2,3,} for a fixed n enters in it together with its Serre dual, an analogue of a principal polarization on an abelian variety. We also identify the isogeny class of each of these formal groups over an algebraically closed field. These results are obtained with the help of the Dieudonné correspondence between bicommutative Hopf algebras and Dieudonné modules. We extend P Goerss’ results on the bilinear products of such Hopf algebras and corresponding Dieudonné modules.


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Victor M Buchstaber. Andrey Lazarev. "Dieudonné modules and $p$–divisible groups associated with Morava $K$–theory of Eilenberg–Mac Lane spaces." Algebr. Geom. Topol. 7 (2) 529 - 564, 2007.


Received: 4 December 2006; Revised: 20 February 2007; Accepted: 8 March 2007; Published: 2007
First available in Project Euclid: 20 December 2017

zbMATH: 1134.55004
MathSciNet: MR2308956
Digital Object Identifier: 10.2140/agt.2007.7.529

Primary: 55N22
Secondary: 14L05

Rights: Copyright © 2007 Mathematical Sciences Publishers


Vol.7 • No. 2 • 2007
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