Appears in collection : Chromatic Homotopy, K-Theory and Functors / Homotopie chromatique, K-théorie et foncteurs

In this work, we start with a new method to adjoin roots to ring spectra. Upon making a new definition of logarithmic THH, we prove that root adjunction is logarithmic THH etale and that it results in interesting splittings in algebraic K-theory. Using this, we obtain new algebraic K-theory computations. This is a joint work with Christian Ausoni and Tasos Moulinos.