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62 votes
8 answers
14k views

Sheaf cohomology and injective resolutions

In defining sheaf cohomology (say in Hartshorne), a common approach seems to be defining the cohomology functors as derived functors. Is there any conceptual reason for injective resolution to come ...
user avatar
28 votes
1 answer
3k views

Two points of view about Borel-moore homology

They are several ways to define the Borel-Moore homology on a locally compact space $X$. The first one is by analogy with the singular homology but instead of using finite chains, we use locally ...
C. Dubussy's user avatar
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11 votes
1 answer
406 views

Resolutions of unbounded complexes: Condition ($\ast$) in Spaltenstein's paper

In the paper "Resolutions of unbounded complexes" (Compositio Math., vol. 65, no. 2, pp. 121-154) N. Spaltenstein generalizes the 6 functor formalism to unbounded complexes of sheaves over ...
algori's user avatar
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