In some cases, it is sufficient to work in the homotopy category Ho(C) associated to a model category C, but looking at the homotopy level alone does not provide us with higher order structure information. Therefore, we investigate the question of rigidity: If we just had the structure of the homotopy category, how much of the underlying model structure can we recover? For example, the stable homotopy category Ho(Sp) has been proved to be rigid by S. Schwede. Moreover, the E(1)-local stable homotopy category, for p=2, has been shown to be rigid by C. Roitzheim. 

 

In this talk, I will discuss a new case of rigidity, which is the localization of spectra with respect to the Morava K-theory K(1), at p=2. While the K(n)-local spectra can be related to the

E(n)-local spectra, there are a lot of main differences to keep in mind while studying the rigidity in the K(1)-local case. Therefore, what might be true and applicable for the E(1)-localization studied by C.Roitzheim might not be true anymore in the K(1)-local world. In this talk, I will emphasis those differences, and sketch the proof of the rigidity of the K(1)-local stable homotopy category at p=2.

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