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

Buchstaber, Victor M; Lazarev, Andrey

doi:10.2140/agt.2007.7.529

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

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

Victor Buchstaber and Andrey Lazarev

Algebraic & Geometric Topology 7 (2007) 529–564

DOI: 10.2140/agt.2007.7.529

arXiv: math.AT/0507036

Abstract

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 ${K {(n)}^{*} K (ℤ, q), q = 2, 3, \dots}$ 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.

Keywords

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

Mathematical Subject Classification 2000

Primary: 55N22

Secondary: 14L05

References

Publication

Received: 4 December 2006

Revised: 20 February 2007

Accepted: 8 March 2007

Published: 10 May 2007

Authors

Victor Buchstaber
Steklov Mathematical Institute Russian Academy of Sciences Gubkina 8 Moscow 119991 Russia
http://www.mi.ras.ru/~buchstab/
Andrey Lazarev
Mathematics Department University of Bristol Bristol BS8 1TW UK
http://www.maths.bris.ac.uk/~maxal/

Volume 7, issue 2 (2007)