Arbeitsgemeinschaft: Elliptic Cohomology according to Lurie

Abstract

In this collection we give an overview of Jacob Lurie's construction of elliptic cohomology and Lubin Tate theory. As opposed to the original construction by Goerss-Hopkins-Miller, which uses heavy obstruction theory, Lurie constructs these objects by a moduli problem in spectral algebraic geometry. A major part of this text is devoted to the foundations and background in higher algebra needed to set up this moduli problem (in the case of Lubin Tate theory) and prove that it is representable.