The Segal conjecture for topological Hochschild homology of Ravenel spectra

In the 1980’s, Ravenel introduced sequences of spectra X(n) and T(n) which played an important role in proof Nilpotence Theorem Devinatz–Hopkins–Smith. present paper, we solve homotopy limit problem for topological Hochschild homology X(n), is a generalized version Segal Conjecture cyclic groups prime order. This result first step towards computing algebraic K-theory using trace methods, approximates sphere spectrum precise sense. We under assumption that canonical map $$T(n)\rightarrow BP$$ commutative ring can be rigidified to $$E_2$$ spectra. show obstruction our holding described terms explicit class Atiyah-Hirzebruch spectral sequence.