Stable homotopy over the derived category

Sunil Chebolu (University of Washington)

It is well known that the stable homotopy category of spectra is formally very similar to the derived category D(R), of a commutative ring R. In view of this, Hopkins, Neeman, Thomason and several others, tried to understand the stable homotopy theory of these derived categories. The structure of these categories is very well understood when the ring R is noetherian, but when R is non-noetherian these categories are very complicated and mysterious. The hope is that a thorough understanding of D(R) for non-noetherian R might shed some new light on the category of spectra.

I will focus on the known results in the noetherian case and explain the dichotomy between the noetherian and non-noetherain worlds. Along the way, a few open problems will also be mentioned.

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