Cyclotomic Frobenius and the Segal conjecture

This talk was given as an attendee at the 2024 Talbot workshop, which was about THH of ring spectra. I gave a proof of the Segal conjecture for \(BP\langle n \rangle\) by first proving it for graded polynomial \(\mathbb{E}_2\)-\(\mathbb{F}_p\)-algebras, and then using (the décalage of) the Adams filtration on \(BP\langle n \rangle\) to reduce to the \(\mathbb{F}_p\)-algebra case. The talk was based on Section 4 of “Redshift and multiplication for truncated Brown-Peterson spectra” by Jeremy Hahn and Dylan Wilson. Notes from all the talks given at Talbot 2024 will eventually be available on the workshop website.