Timeline for Representing $j_*\mathcal{O}_U$ as filtered colimit of perfect complexes
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Jun 28, 2019 at 6:09 | comment | added | Denis Nardin | @crystalline It seems to me that if I manage to prove that $R\pi_*\mathcal{O}$ is perfect, the proof is complete though (since $U$ is an effective Cartier divisor in $\tilde X$). Do you agree? | |
| Jun 27, 2019 at 16:39 | comment | added | crystalline | I mistyped (you understood but just to clarify), I meant it does not preserve perfect complexes without further hypotheses | |
| Jun 27, 2019 at 16:21 | history | edited | Denis Nardin | CC BY-SA 4.0 |
I'm an idiot and I confused above and below twice
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| Jun 27, 2019 at 15:26 | comment | added | Denis Nardin | @crystalline Ugh.. I misunderstood theorem 2.5.4 in Thomason-Trobaugh | |
| Jun 27, 2019 at 15:07 | comment | added | crystalline | @DenisNardin $p_*$ does not preserve perfect complexes under further hypotheses (finite Tor-amplitude, or domain and codomain regular). If you can choose $i$ to be a regular immersion (I guess this should be possible but not sure without checking) then the projection of the blowing up would be lci so that would suffice. | |
| Jun 27, 2019 at 11:06 | history | edited | Denis Nardin | CC BY-SA 4.0 |
Correct confusion between above & below..
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| Jun 27, 2019 at 10:55 | history | edited | Denis Nardin | CC BY-SA 4.0 |
deleted 6 characters in body
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| Jun 27, 2019 at 10:47 | comment | added | Sasha | I am not sure how useful it is, but you can try the following standard construction. Let $\tilde{X}$ be the blowup of the complement of $U$ in $X$. Then the map $j$ decomposes as $\pi \circ i$, where $i \colon U \to \tilde{X}$ and $\pi$ is the blowup. The point is that $i$ is affine, so $Ri_* = i_*$, and $\pi$ is projective, so you can use a relative Cech complex to compute $R\pi_*$. | |
| Jun 27, 2019 at 10:42 | history | asked | Denis Nardin | CC BY-SA 4.0 |