Could someone give an overview, or just some examples, of "finiteness conditions" for simplicial sheaves/presheaves and/or simplicial schemes? Any answer or comment about this would be interesting, ...
Give an example of a stack X with affine stabilizer groups and separated but not quasi-affine diagonal. Remarks: 1) If X has finite stabilizer groups then the diagonal is quasi-finite and separated, ...
Is there an example of an algebraic stack whose closed points have affine stabilizers but whose diagonal is not affine?
Burt Totaro has a result that for a certain class of algebraic stacks, having affine diagonal is equivalent to the stabilizers at closed points begin affine. Is there an example of this equivalence ...