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Is there a name/description in standard terms of the class of morphisms of schemes defined by the following property: the inverse image of any affine open is contained in an affine open?

It should be distinct from affine morphisms (as can be seen by considering the inclusion of affine plane in affine plane with origin doubled).

The reason I am asking is that the stalks of pushforwards of quasi-coherent sheaves could be computed in a certain way for such morphisms.

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  • $\begingroup$ Quasi-affine morphisms? $\endgroup$
    – Mohan
    Commented Mar 24, 2019 at 2:23
  • $\begingroup$ @Mohan stacks project says quasi-affine morphisms are required to be quasi-compact; but yes, this is close enough I would say $\endgroup$
    – user137400
    Commented Mar 24, 2019 at 6:42

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