A proof of the existence of level 1 elliptic cohomology

Hovey, Mark A.

doi:10.1090/S0002-9939-1993-1156469-7

A proof of the existence of level $1$ elliptic cohomology
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Proc. Amer. Math. Soc. 118 (1993), 1331-1334 Request permission

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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