Timeline for Is Serre duality related to Pontryagin duality?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Sep 10, 2018 at 4:36 | comment | added | skd | Roughly speaking, one instance of such a relationship comes from the fact that the dualizing sheaf (in the sense of Grothendieck) for Spec Z is the injective Z-module Q/Z. | |
| Aug 13, 2018 at 0:08 | comment | added | Bombyx mori | @NostradamusJR: I meant something along the lines $R(F\circ G)\cong RF\circ RG$, I learned it from math.uchicago.edu/~may/REU2013/REUPapers/Fung.pdf. | |
| Aug 13, 2018 at 0:03 | comment | added | Bernie | What is "Gronthendieck duality"? | |
| Aug 12, 2018 at 23:39 | comment | added | Bombyx mori | @ArunDebray: I have read quite a bit on Ising model, and I have read some of Daniel Freed's papers. However the specific paper you quoted is unreadable to me. I am kind of lost with notation. So I am looking for a specific 2D example. | |
| Aug 12, 2018 at 23:37 | comment | added | Bombyx mori | @DonuArapura: I am actually looking for something quite modest. As a first approximation, Poincare duality can be interpreted as cup product of differential forms is non-degenerate. Is there something similar using Fourier transform? I am not entirely sure what Fourier transform of a differential form should be, for example. | |
| Aug 12, 2018 at 18:36 | history | edited | Danny Ruberman | CC BY-SA 4.0 |
replaced "rhetoric" with "theoretic" (although I was amused by the original wording!)
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| Aug 12, 2018 at 13:10 | comment | added | Arun Debray | @DonuArapura in full generality it's probably not written down, but there's a version of this "Poincaré-Pontrjagin duality" in this paper by Freed-Teleman (e.g. just after (3.32)). | |
| Aug 12, 2018 at 12:37 | comment | added | Donu Arapura | When I was in grad school, I took a topology class from John Morgan, where he explained how to formulate Poincaré duality with coefficients in a locally compact abelian group; the other side takes values in the Pontryagin dual. (I'm not sure it's written any place.) I can imagine a similar set up for Serre duality, but this seems different from what you're asking about. | |
| Aug 12, 2018 at 6:32 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
edited tags; Pontragin -> Pontryagin
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| Aug 12, 2018 at 6:24 | history | edited | Bombyx mori | CC BY-SA 4.0 |
added 150 characters in body
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| Aug 12, 2018 at 6:17 | history | asked | Bombyx mori | CC BY-SA 4.0 |