The isomorphism of the towers and chromatic homotopy theory

n stable homotopy theory, one attempts to understand the category of spectra. This category is morally akin to the derived category of abelian groups. But it lends itself to a form of localization that is not available in classical algebra - chromatic localization. The study of chromatically localized spectra is central to stable homotopy theory. I will explain a novel approach for such study (pioneered by Barthel-Schlank-Stapleton-Weinstein): the use of the isomorphism of the Lubin-Tate and Drinfeld towers of rigid analytic geometry. I shall explain a structural result, accounting for much of the rational behavior of chromatically localized spectra, obtained in collaboration with Shay Ben-Moshe.