# Deeper Kummer theory

### APA

Johnson-Freyd, T. (2023). Deeper Kummer theory. Perimeter Institute. https://pirsa.org/23090104

### MLA

Johnson-Freyd, Theo. Deeper Kummer theory. Perimeter Institute, Sep. 21, 2023, https://pirsa.org/23090104

### BibTex

@misc{ pirsa_PIRSA:23090104, doi = {10.48660/23090104}, url = {https://pirsa.org/23090104}, author = {Johnson-Freyd, Theo}, keywords = {Mathematical physics}, language = {en}, title = {Deeper Kummer theory}, publisher = {Perimeter Institute}, year = {2023}, month = {sep}, note = {PIRSA:23090104 see, \url{https://pirsa.org}} }

Theo Johnson-Freyd Dalhousie University

## Abstract

A tower is an infinite sequence of deloopings of symmetric monoidal ever-higher categories. Towers are places where extended functorial field theories take values. Towers are a "deeper" version of commutative rings (as opposed to "higher rings" aka E∞-spectra). Notably, towers have their own opinions about Galois theory, and think that usual Galois groups are merely shallow approximations of deeper homotopical objects. In this talk, I will describe some steps in the construction and calculation of the deeper Galois group of a characteristic-zero field. In particular, I'll explain a homotopical version of the Kummer description of abelian extensions. This is joint work in progress with David Reutter.

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Zoom link: https://pitp.zoom.us/j/97950701035?pwd=Wk9FRSt2MkN3eWptTVltRVJncnFHdz09