Localization sequences for logarithmic topological Hochschild homology
  We study the logarithmic topological Hochschild homology of ring spectra with logarithmic structures and establish localization sequences for this theory. Our results apply, for example, to connective covers of periodic ring spectra like real and complex topological K-theory. 
John Rognes, Steffen Sagave, Christian Schlichtkrull
math.AT math.KT