elliptic spectrum in nLab

Contents

Contents

Idea

An elliptic spectrum is a spectrum which represents an elliptic cohomology theory.

Definition

For EE a ring spectrum, write E •(*)E^\bullet(\ast) for its coefficient ring and generally E •(X)E^\bullet(X) for its generalized cohomology ring over any XX.

This is due to (Ando-Hopkins-Strickland01, def. 1.2). See for instance also (Gepner 05, def. 15).

• elliptic cohomology, elliptic genus, tmf

• Eilenberg-MacLane spectrum

• K3-spectrum

References

The concept of elliptic spectrum was introduced in

• Matthew Ando, Michael Hopkins, Neil Strickland, Elliptic spectra, the Witten genus, and the theorem of the cube, Inventiones Mathematicae, 146:595–687, 2001, (pdf, doi:10.1007/s002220100175)

A brief review is for instance in of

• David Gepner, section 1 of Homotopy topoi and equivariant elliptic cohomology, 2005.

Survey includes

• Jacob Lurie, A Survey of Elliptic Cohomology

• Charles Rezk, Elliptic cohomology and elliptic curves, Felix Klein Lectures, Bonn 2015 (web)