Timeline for Coinflation in cohomology
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Nov 22, 2017 at 9:37 | comment | added | Chris Wuthrich | One candidate that could be named coinf is the map $H^{n-i}(G,A)\to H^i(G/H,D_n(H,A))^{\vee}$ where $\vee$ is the Pontryagin dual and $D_n(H,A)$ is the inductive limit of $H^n(U,A)^{\vee}$ as $U$ runs through subgroups of $G$ containing $H$. The dual of this map appears in Tate's spectral sequence together with the dual of the corestriction map, just like inf and res do in the Hochschild-Serre spectracl sequence. (Cohomology of number fields II.5.4) | |
| Nov 22, 2017 at 4:19 | comment | added | Chris Gerig | You’re right! And inflation does not exist on homology. I think this boils down to an issue with the map on group rings $\mathbb{Z}[G]\to\mathbb{Z}[G/H]$. All the other maps use functoriality of (co)homology (in both variables: groups and modules) and Shapiro’s lemma associated to (co)extension of scalars coming from inclusion of H into G. | |
| Nov 22, 2017 at 3:24 | review | Close votes | |||
| Nov 22, 2017 at 13:07 | |||||
| Nov 22, 2017 at 3:18 | history | edited | HASouza | CC BY-SA 3.0 |
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| Nov 22, 2017 at 3:10 | comment | added | HASouza | @ChrisGerig I haven't been so lucky, the first 5 pages of a search for "coinflation on cohomology" only shows coinflation defined at homology, not cohomology groups. Same goes for "$\text{coinf}$" references on Weibel's book, all three appearances refer to maps defined on group homology rather than cohomology. | |
| Nov 21, 2017 at 22:15 | history | edited | HASouza |
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| Nov 21, 2017 at 22:12 | review | First posts | |||
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| Nov 21, 2017 at 22:09 | history | asked | HASouza | CC BY-SA 3.0 |