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Serre dimension and stability conditions Takahashi, Atsushi


We study the scaling dimension (or the similarity dimension) of the perfect derived category of a smooth compact dg algebra called the Serre dimension. It is expected that the infimum of the Ikeda-Qiuâ s global dimsion function on the space of stability conditions also gives another â goodâ notion of dimension. One of our results is that its infimum is always greater than or equal to the Serre dimension. Motivated by the ADE classification of the 2-dimensional N=2 SCFT with \widehat{c}<1, we also give a characterization of the derived category of Dynkin quivers in terms of the Serre dimension and the global dimension function. This is a joint work in progress with Kohei Kikuta and Genki Ouchi.

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