Timeline for Leopoldt's conjecture and cup-products
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Apr 10, 2012 at 2:01 | history | edited | Filippo Alberto Edoardo | CC BY-SA 3.0 |
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| Apr 10, 2012 at 1:49 | history | edited | Filippo Alberto Edoardo | CC BY-SA 3.0 |
(Hopefylly) corrected argument for $\chi\neq 1$.
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| Apr 9, 2012 at 16:20 | comment | added | Filippo Alberto Edoardo | Dear Joël, I see the issue with Inf-Res that I thought would have been trivial – I am sorry. I will try to write down a proper proof, if I can and come back if I have it. | |
| Apr 9, 2012 at 13:34 | comment | added | Joël | Dear Filippo, I am not sure I completely get the argument yet. Already in your answer, second part, how do you prove that you can reduce to the case of Delta ? | |
| Apr 9, 2012 at 0:27 | comment | added | Filippo Alberto Edoardo | Dear Joël, for the cyclotomic character you get 0 again, I guess. My argument shows that you reduce to Gamma-cohomology, and H^2 is zero bacuase cd(Gamma)=1. I actually think this restriction is not severe, you might always write the Galois group on which chi acts faithfully as product of something free (of dim. 1) and something finite. Then both H^2 with Z_p-coefficients are trivial. Or am I wrong? | |
| Apr 8, 2012 at 16:51 | comment | added | Joël | Dear Filippo, thank you very much. Actually I had arrived at the same conclusion a few weeks ago (with my student Yu Fang) that for a finite order character the cup product was always zero (with a proof very close to yours). But the method does not seem to generalize to infinite-order characters. For example, what about $\chi=$ cyclotomic character ? I don't know how to do it, nor any infinite-order character for that matter. | |
| Apr 8, 2012 at 2:04 | history | edited | Filippo Alberto Edoardo | CC BY-SA 3.0 |
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| Apr 8, 2012 at 1:58 | history | edited | Filippo Alberto Edoardo | CC BY-SA 3.0 |
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| Apr 8, 2012 at 1:45 | history | answered | Filippo Alberto Edoardo | CC BY-SA 3.0 |