Examples of chromatic redshift in algebraic K-theory

We give a simple argument to detect chromatic redshift in the algebraic K -theory of E_ -ring spectra and give two applications: we show for n 1 that K (E₍), the algebraic K -theory of any height n Lubin–Tate theory, has nontrivial T (n+1) -localization, and that K^ (n) (k), the n -fold iterated algebraic K -theory of a field k of characteristic different from the implicit prime p, has nontrivial T (n) -localization.