# On the stable homotopy theory of stacks and elliptic cohomology

### APA

Gepner, D. (2016). On the stable homotopy theory of stacks and elliptic cohomology. Perimeter Institute. https://pirsa.org/16040082

### MLA

Gepner, David. On the stable homotopy theory of stacks and elliptic cohomology. Perimeter Institute, Apr. 21, 2016, https://pirsa.org/16040082

### BibTex

@misc{ pirsa_PIRSA:16040082, doi = {10.48660/16040082}, url = {https://pirsa.org/16040082}, author = {Gepner, David}, keywords = {Mathematical physics}, language = {en}, title = {On the stable homotopy theory of stacks and elliptic cohomology}, publisher = {Perimeter Institute}, year = {2016}, month = {apr}, note = {PIRSA:16040082 see, \url{https://pirsa.org}} }

Purdue University

Talk Type

**Subject**

Abstract

In this talk, we'll discuss what it means to be a cohomology theory for topological stacks, using a notion of local symmetric monoidal inversion of objects in families. While the general setup is abstract, it specializes to many cases of interest, including Schwede's global spectra. We will then go on to discuss various examples with particular emphasis on elliptic cohomology. It turns out that TMF sees more objects as dualizable (or even invertible) than one might naively expect.