Stability conditions on affine Noetherian schemes

Kotaro Kawatani

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arXiv · 2009.14466

Stability conditions on affine Noetherian schemes

Kotaro Kawatani

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Abstract

We show that the existence of locally finite stability conditions on the bounded derived category $\mathbf{D}^{b}(X)$ of coherent sheaves on an affine Noetherian scheme $X$ is equivalent to $\dim X=0$. We also study the spaces of stability conditions on the category of morphisms $\mathbf M_{X}$ in the derived category of the scheme $X$ and show that the spaces of stability conditions on $\mathbf{D}^{b}(X)$ and $\mathbf{M}_{X}$ are homotopy equivalent to each other.

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BibTeX RIS

Kotaro Kawatani. 2020-09-30. Stability conditions on affine Noetherian schemes. https://arxiv.org/abs/2009.14466

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