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

 

A proof of the existence of level $ 1$ elliptic cohomology


Author: Mark A. Hovey
Journal: Proc. Amer. Math. Soc. 118 (1993), 1331-1334
MSC: Primary 55N22; Secondary 11F75
MathSciNet review: 1156469
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Abstract: Landweber provided two proofs of the existence of (level 2) elliptic cohomology (Lecture Notes in Math., vol. 1326, Springer-Verlag, New York, 1988, pp. 69-93). As Baker pointed out (J. Pure Appl. Algebra 63 (1990), 1-11), one of these proofs gives a level 1 elliptic cohomology theory as well. In this note we provide an alternative proof of the existence of level 1 elliptic cohomology. The idea here is to use Landweber's direct proof of the existence of level 2 elliptic cohomology and an integrality argument to deduce the existence of level $ 1$ elliptic cohomology from that.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1156469-7
PII: S 0002-9939(1993)1156469-7
Article copyright: © Copyright 1993 American Mathematical Society