A PROOF OF THE EXISTENCE OF LEVEL 1 ELLIPTIC COHOMOLOGY

Landweber provided two proofs of the existence of (level 2) elliptic c ohomology (Lecture Notes in Math., vol. 1326, Springer-Verlag, New Yor k, 1988, pp. 69-93). As Baker pointed out (J. Pure Appl. Algebra 63 (1 990), 1-11), one of these proofs gives a level 1 elliptic cohomology t heory as well. In this note we provide an alternative proof of the exi stence of level 1 elliptic cohomology. The idea here is to use Landweb er's direct proof of the existence of level 2 elliptic cohomology and an integrality argument to deduce the existence of level 1 elliptic co homology from that.