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The Stacks project

History of tag 09V3

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type time link
changed the statement 2016-11-07 3b84fd2
Fix compile problem
changed the statement and the proof 2016-11-07 2fcc073
Upgrade proper base change theorem in topology

Thanks to Brian Conrad who writes

"Johan, I noticed that the Stacks Project has a proper base change theorem
in topology, but it is plagued by unnecessary hypotheses.  In
SGA4, Exp. V_{bis}, 4.1, 4.2 Deligne gives a very slick proof of that
base-change isomorphism for proper maps between arbitrary topological
spaces, where proper := separated + universal closed =
separated + closed + compact fibers.  This generality deserves to be
more widely known."

The proof in the Stacks project is not as slick because we don't use the
notion of "mou" sheaves. (Wikipedia says "mou" = "soft".) Our approach
uses Cech cohomology and therefore needs some lemmas on the existence of
suitable open coverings...
assigned tag 09V3 2013-12-27 778cafd
Tags: Added new tags
created statement with label lemma-cohomology-of-closed in cohomology.tex 2013-12-27 3ea6703
Cohomology on locally compact spaces

We continue with the somewhat awkward terminology where we say
"Hausdorff and locally quasi-compact" in stead of "locally compact".