Morphisms of Finite Flat Dimension

Lemma 26.4 (Projection Formula). Assume that /, is concentrated. Then the natural map 

Utilizing the commutativity as in the proof of Lemma 26.4 and Lemma 18.7, it is not so difficult to show the following. 

As T is constructed from ( and d by definition, the assertion follows easily from Lemma 26.8 and Lemma 26.9.  

By Lemma 26.11, x(/ ) an isomorphism if and only if there exists some compactification /, = q,j such that is an isomorphism. 

be a compactification of /,. It suffices to show that x p fl ) is an isomorphism. In view of Lemma 26.7, we may assume that F = Oy,. Then in view of Proposition 18.14 and Lemma 26.6, it suffices to show that 

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