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Apr 29, 2013 at 16:23 vote accept Jakob
Jul 30, 2012 at 9:14 comment added Jakob Yes, I hope the parenthetical addition makes it clearer. Indeed, I also don't expect the converse to be true, but I'm looking for a statement that is (true and) somehow close, in spirit, to the converse statement. I.e. I am looking for "Assuming $f^! R = R[n]$, then $M$ is "nice" in some sense."
Jul 29, 2012 at 18:53 answer added Liviu Nicolaescu timeline score: 5
Jul 29, 2012 at 17:05 comment added Konrad Voelkel May I suggest you to edit the question to include some conjectural "converse statement"? It took me some time to figure out you probably want something like "if the exceptional inverse image along the constant map is just a shifted-by-dimension constant sheaf, the manifold is smooth". I would guess this is wrong, but I'm not an expert.
Jul 29, 2012 at 14:52 history edited Jakob CC BY-SA 3.0
clarify question
Jul 27, 2012 at 19:11 history asked Jakob CC BY-SA 3.0