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user137767
user137767

I think that theThe category of coherent sheaves on a locally Noetherian scheme is abelian (maybe the scheme has to be qcqs, I am bad with schematic monsters). Are there some geometric conditions on the scheme that imply that the category of coherent sheaves is semisimple?

Edited in response to posic's comments.

I think that the category of coherent sheaves on a scheme is abelian (maybe the scheme has to be qcqs, I am bad with schematic monsters). Are there some geometric conditions on the scheme that imply that the category of coherent sheaves is semisimple?

The category of coherent sheaves on a locally Noetherian scheme is abelian. Are there some geometric conditions on the scheme that imply that the category of coherent sheaves is semisimple?

Edited in response to posic's comments.

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user137767
user137767

Semisimplicity of the category of coherent sheaves?

I think that the category of coherent sheaves on a scheme is abelian (maybe the scheme has to be qcqs, I am bad with schematic monsters). Are there some geometric conditions on the scheme that imply that the category of coherent sheaves is semisimple?