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There should be a separate page for discussing dualizing complexes in the context of algebraic geometry. A good *new* reference for the subject is contained in https://www.math.bgu.ac.il/~amyekut/teaching/2016-17/der-cats-IV/public63.pdf He constructs the dualizing complex for commutative rings on the bottom of page 218 and the top of 219.
It's very easy to derive the property as stated now . I therefore *assume* that the version stated before (with ! and * intertwined) was simply a typo, but I'm quite ignorant about these things. Any objections to the change? Amitushtush (talk) 23:36, 21 February 2018 (UTC)
I think "If X is a finite-dimensional locally compact space..." needs to be clarified. What does finite dimensionality mean? I assume some sort of cohomological finiteness...? Amitushtush (talk) 23:55, 21 February 2018 (UTC)
According to Sheaves On Manifolds (Kashiwara & Schapira, 1990) Definition 3.1.16(i) & (ii) on page 148 the assumptions are that the space is locally compact and Hausdorff, has finite cohomological dimension, and that the space X has finite c-soft dimension (page 133 exercise 9(b); partially defined by exercise 9(a)). A c-soft sheaf (defined on page 104) is a compact analogue of flabby (or sometimes flasque) sheaf.
Gobal Verdier duality involves a comparison of homsets in a derived category which in general might not be actual "sets" in the conventional sense as derived categories are usually by construction "large" categories (relative to a fixed universe). i.e. the derived category in general isn't locally small. If it is necessary it might be good to add a note that this result could rely on more than ZF by requiring the existence of at least one (strongly) inaccessible cardinal. I believe it is referred to by some as the "Grothendieck axiom".