Dieudonné modules and p–divisible groups associated with Morava K–theory of Eilenberg–Mac Lane spaces

Buchstaber, Victor M¹ ; Lazarev, Andrey²

¹Steklov Mathematical Institute, Russian Academy of Sciences, Gubkina 8 Moscow 119991, Russia
²Mathematics Department, University of Bristol Bristol BS8 1TW, UK

Algebraic and Geometric Topology, Tome 7 (2007) no. 2, pp. 529-564

Résumé

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(ℤ,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.

Détail

DOI : 10.2140/agt.2007.7.529

Keywords: Hopf ring, Dieudonné module, Morava $K$–theory, $p$–divisible group, Serre duality

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