Stability conditions on affine Noetherian schemes

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.

13 pages, v3: Title has been changed

References in corpus (1)

• Markov convexity and local rigidity of distorted metrics