Timeline for Most general form of Poincaré duality in étale cohomology
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Nov 19, 2021 at 1:57 | comment | added | user30211 | Thank you all for your contributions. | |
| Nov 15, 2021 at 9:51 | comment | added | David Hansen | If you really want the most general statement, look at Theorem 0.1.4 here (arxiv.org/pdf/1211.5948.pdf). | |
| Nov 15, 2021 at 9:30 | comment | added | Denis Nardin | Relevant paper | |
| Nov 15, 2021 at 8:58 | history | edited | YCor | CC BY-SA 4.0 |
added tag, formatting
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| S Nov 15, 2021 at 8:46 | history | edited | Glorfindel | CC BY-SA 4.0 |
more specific title
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| S Nov 15, 2021 at 8:46 | history | suggested | adverse sheaf | CC BY-SA 4.0 |
better title?
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| Nov 15, 2021 at 4:46 | review | Suggested edits | |||
| S Nov 15, 2021 at 8:46 | |||||
| Nov 14, 2021 at 13:54 | comment | added | A.B. | An easy to navigate reference for this is [Etale cohomology theory, 8.2, 8.3 and 8.5] by Lei Fu. | |
| Nov 14, 2021 at 13:50 | comment | added | A.B. | As I understand it, Poincaré duality in étale cohomology comes down to the existence of a suitable trace morphism $Tr_f: Rf_{!}f^{\ast}L(d)[2d]\to L$ for a smooth morphism $f:X\to Y$ pure of relative dimension $d$ and a torsion complex $L$ on $Y$. The trace morphism is constructed, by devissage, from the case of a smooth irreducible projective curve $X$ over an algebraically closed field, where it is taken to be the degree map $\deg: Pic(X)\to \mathbb{Z}$ modulo $n$. | |
| Nov 14, 2021 at 9:57 | comment | added | David Roberts♦ | @A.B. I would assume it means a setup that is as general as possible, or, equivalently, with the fewest restrictions/assumptions. Not in a technical sense of 'generic', as happens in algebraic geometry, for instance. | |
| Nov 13, 2021 at 23:40 | comment | added | user30211 | @A.B. As a rule of thumb, if two mathematicians choose two categories in different rooms and you can name an essentially surjective functor from one setup $A$ to the other $B$, then $A$ is more generic. The same principle works for $2$-categorical logic, which is the foundations on my computer right now. We might like to speak of the most generic setup when we want to isolate what worked about an idea. I've heard that called sifting in some places. | |
| Nov 13, 2021 at 23:13 | comment | added | A.B. | Can you clarify (for us non english-speaking natives), what you mean by "the most generic situation" ? | |
| Nov 13, 2021 at 21:30 | history | asked | user30211 | CC BY-SA 4.0 |