Deeper Kummer theory


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


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


          @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



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.


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