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(Eₙ) , 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.