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Nov 30, 2023 at 22:39 comment added OrdinaryAnon Thank you for your input. I'll be sure to check out the article!
Nov 30, 2023 at 10:28 comment added Nicolas Hemelsoet @OrdinaryAnon : I agree that more details would have been nice there. I added a few details to my answer but I don't know how write a rigorous proof myself.
Nov 30, 2023 at 10:26 history edited Nicolas Hemelsoet CC BY-SA 4.0
added 940 characters in body
Nov 29, 2023 at 19:03 comment added OrdinaryAnon Sadly I don't follow his explanation there. Specifically, I mean the fact that $f^!(F) \cong f^*(F) \otimes f^!(\mathcal{O}_Y)$, for $F$ with proper support. As far as the spanning set is concerned, I only know a proof that they are in fact one when the scheme is smooth and projective. In the general case $Y$ is only quasi-projective, I think.
Nov 29, 2023 at 17:41 history answered Nicolas Hemelsoet CC BY-SA 4.0