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Stability conditions on twisted derived categories I: Existence and full numerical support

Contributed by Zhirui Li

We prove that for every nonempty smooth projective variety $X$ over an arbitrary field and every Brauer class $\alpha$ , the twisted derived category $\mathrm{D}^b(X,\alpha)$ admits a Bridgeland stability condition with full numerical support. Based on Chunyi Li's construction and its extension to arbitrary fields, we establish uniform phase control under tensoring by an Azumaya algebra and calibrate the resulting slicing to the induced central charge. We further show that the constructed stability condition is geometric and satisfies a mass-Hom bound, which persists throughout its connected component.

Author comments: 26 pages. Comments and suggestions are welcome.

Primarily human-written textHuman understanding: all partsBridgeland stability conditions; twisted derived categories

Nov 12, 202626 pages

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Stability conditions on twisted derived categories I: Existence and full numerical support

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