Postdoc day, Seminar 1: Adjoining roots to ring spectra and algebraic K-theory

Date: 2022-02-18

Time: 13:30 - 14:00


Özgür Bayindir


In this work, we start with a new method to adjoin roots to E_2 ring spectra.  We prove that this process is logarithmic THH ‘etale and that it results in interesting splittings in algebraic K-theory. For instance, we obtain that T(n+1)-locally, the algebraic K-theory of the nth Morava E-theory contains the algebraic K-theory of the truncated Brown-Peterson spectrum with coefficients as a summand. In particular, this provides a proof of the fact that Morava E-theories satisfy the redshift conjecture. This is a joint work with Tasos Moulinos and Christian Ausoni.