Timeline for Pontryagin dual of cokernel, $(\operatorname{coker} F)^* \cong \hat{H}^0(\operatorname{Gal}(L/K),E(L)), $
Current License: CC BY-SA 4.0
29 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 28, 2023 at 17:27 | vote | accept | Duality | ||
| Sep 28, 2023 at 16:46 | history | edited | Michael Hardy | CC BY-SA 4.0 |
proper use of \operatorname
|
| Sep 28, 2023 at 7:08 | answer | added | Mikhail Borovoi | timeline score: 3 | |
| Sep 28, 2023 at 4:45 | comment | added | Duality | I am very much looking forward to your suggestion. Thank you in advance. | |
| Sep 27, 2023 at 19:01 | comment | added | Mikhail Borovoi | You nee a map. I will type it tomorrow. | |
| Sep 27, 2023 at 18:11 | comment | added | Duality | I mean the former. | |
| Sep 27, 2023 at 18:09 | history | edited | Duality | CC BY-SA 4.0 |
added 2 characters in body; edited title
|
| Sep 27, 2023 at 18:05 | comment | added | Mikhail Borovoi | What is ${coker} F^*$? Do you mean $({\rm coker}\, F)^*$ of ${\rm coker}( F^*)$ ? | |
| Sep 27, 2023 at 17:54 | history | edited | Duality | CC BY-SA 4.0 |
added 334 characters in body
|
| Sep 27, 2023 at 17:53 | comment | added | Duality | The notation used in this question is somewhat different from that of the paper. However, this question is still self-contained. I have provided a link to the paper for reference, but there is no mention of the isomorphism discussed in this question in the paper, even though it's described using slightly different notation. | |
| Sep 27, 2023 at 17:36 | comment | added | Duality | @Mikhail Borovoi Sorry, it is lemma 5. Lemma 4 has nothing to do with this question. | |
| Sep 27, 2023 at 17:35 | history | edited | Duality | CC BY-SA 4.0 |
edited body
|
| Sep 27, 2023 at 16:30 | comment | added | Mikhail Borovoi | Lemma 4 on page 214 in the linked paper is indeed easy (though not obvious). If this is what you need, I can type a proof. | |
| Sep 27, 2023 at 16:01 | comment | added | Mikhail Borovoi | What is $F$? Is it related with $\mathcal F$ in the linked paper? | |
| Sep 27, 2023 at 16:00 | comment | added | Mikhail Borovoi | What is the relation between $L_w$ and $L_{v_L}$? | |
| Sep 27, 2023 at 14:31 | comment | added | Duality | Sorry, I added some information. Thank you very much. | |
| Sep 27, 2023 at 14:30 | history | edited | Duality | CC BY-SA 4.0 |
added 44 characters in body
|
| Sep 27, 2023 at 14:23 | comment | added | Mikhail Borovoi | If you indeed want to get an answer, please write your question with more details. What is $E$? | |
| Sep 27, 2023 at 14:21 | comment | added | Mikhail Borovoi | Is $L/K$ a quadratic extension? If not, then your definitions of the trace map and the Tate cohomology is wrong! | |
| Sep 27, 2023 at 9:36 | history | edited | Duality | CC BY-SA 4.0 |
deleted 83 characters in body; edited title
|
| Sep 27, 2023 at 7:21 | comment | added | Duality | Thank you for your reaction. I added the N.B. in the bottom of my question. | |
| Sep 27, 2023 at 7:19 | history | edited | Duality | CC BY-SA 4.0 |
added 290 characters in body
|
| Sep 27, 2023 at 6:32 | comment | added | მამუკა ჯიბლაძე | Could you be more specific? Which place on page 214 of that paper do you mean? It is all quite confusing for me since the Pontryagin dual in that paper is denoted by $(-)^*$ and there is no such thing on page 214; while there are lots of hats, and hat in that paper denotes profinite completion rather than Pontryagin dual as in your question. | |
| Sep 27, 2023 at 6:09 | history | edited | Duality | CC BY-SA 4.0 |
added 100 characters in body
|
| S Sep 26, 2023 at 5:53 | history | edited | Michael Hardy | CC BY-SA 4.0 |
typo in the title
|
| S Sep 26, 2023 at 5:53 | history | suggested | Anurag Sahay | CC BY-SA 4.0 |
typo in the title
|
| Sep 26, 2023 at 5:31 | review | Suggested edits | |||
| S Sep 26, 2023 at 5:53 | |||||
| Sep 26, 2023 at 4:48 | history | edited | მამუკა ჯიბლაძე | CC BY-SA 4.0 |
typo
|
| Sep 26, 2023 at 4:28 | history | asked | Duality | CC BY-SA 4.0 |