The Stacks project

Two typos in perfect

Better Ext + f^*F

Could have been said ages ago...

Cohomology and base change -- more general

This is better but also worse bc harder to read...

Fix an error

While reviewing the material on cohomology and base change we found
a mistake in the proof of Lemma lemma-base-change-RHom. The mistake is
fatal in the sense that we don't know if the result is true as it was
stated. The fix is to assume that the object E is a perfect complex (as
opposed to just pseudo-coherent).

We also reorganized the material somewhat. We intend to add a fifth
section on cohomology and base change in the near future (removing some
of the Noetherian hypotheses by limit arguments).

Base change for RHom

This time for algebraic spaces.

Tags: Added new tags

Also fixed some references

Cohomology and base change, IV

This time for algebraic spaces.

An example of a group scheme which is not quasi-separated

Clean up the material from last commit

The claims on duals of pseudo-coherent complexes were too optimistic. As
a replacement we directly construct a base change map for pushforwards
of internal homs. Then we show this is a qis by the induction principle.

We also fixed the proof of the lemma on duals of perfect objects as the
previous one was nonsense.

Finally, we improve the (trivial) lemma on vanishing of Ext groups
between objects of the derived category.

Base change for Rf_*RHom(E, G)

Holds very generally when f is qc + qs and E is pseudo-coherent and G is
quasi-coherent and flat over the base. This really clears up the air!