Timeline for What are "packets"?
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 31, 2017 at 18:05 | vote | accept | john mangual | ||
| Oct 31, 2017 at 18:01 | answer | added | Ilya Khayutin | timeline score: 10 | |
| Oct 27, 2017 at 7:31 | comment | added | David Roberts♦ | @LSpice thanks for demystifying a piece of terminology that while sounding profound and mystical, is now obvious. Next people will be talking about the "set/space of L-packets", no doubt... | |
| Oct 27, 2017 at 2:10 | comment | added | LSpice | @johnmangual, I'm sorry; I meant that the text explains what is meant by class number 1, not that it's obvious what that has to do with number-field class numbers. For $\mathbf G = \mathrm{GL}_1$, the double-coset space is $\mathbb Q^\times\backslash\mathbb A^\times/\mathbb Q_S^\times\mathbb Z^S$. I guess, but don't know for sure, that the size of (the analogue for other number fields of) this is (or at least is related to) the class number. | |
| Oct 27, 2017 at 0:51 | comment | added | reuns | Did you read Silverman ATAEC chapter II on how to find the minimal polynomial of $j(E)$ for $E$ an elliptic curve with complex multiplication (the first step towards class field theory) ? | |
| Oct 26, 2017 at 23:36 | answer | added | paul garrett | timeline score: 2 | |
| Oct 26, 2017 at 22:43 | comment | added | john mangual | I thought class number 1 had to do with factorization in number fields. That's not self-explaining at all. | |
| Oct 26, 2017 at 22:16 | comment | added | LSpice | (P.S. I don't know anything about packets of CM points, but, as someone involved with the Langlands correspondence, to me 'packet' means "I wish that I had a bijection but I don't, and I don't like the term 'fibre'" :-). Maybe it is so here, too.) | |
| Oct 26, 2017 at 22:14 | comment | added | LSpice | The wording regard torus orbits in the current version of the paper is slightly different from what you have written, but I am not sure clearer. An algebraic (maximal) torus in $\mathrm{PGL}_2$ is a conjugate in $\mathrm{PGL}_2(\overline{\mathbb Q})$ of the group of diagonal matrices in $\mathrm{PGL}_2$. For example, $\left\{\begin{pmatrix} a & 0 \\ 0 & d \end{pmatrix}\right\}$ and $\left\{\begin{pmatrix} a & b \\ -b & a \end{pmatrix}\right\}$ are such tori in $\mathrm{PGL}_2$. They are conjugate over $\overline{\mathbb Q}$, in an obvious sense, but not over $\mathbb Q$. | |
| Oct 26, 2017 at 22:11 | comment | added | LSpice | The class-number-1 description seems self-describing, right? It says that there is only one $(\mathbf G(\mathbb Q), \mathbf G(\mathbb Q_S)\cdot K^S)$-double coset in $\mathbf G(\mathbb A)$, which means that $\mathbf G(\mathbb A)$ is the set product $\mathbf G(\mathbb Q)\cdot(\mathbf G(\mathbb Q_S)\cdot K^S)$. | |
| Oct 26, 2017 at 20:45 | history | edited | john mangual | CC BY-SA 3.0 |
Translate from Adeles ?
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| Oct 26, 2017 at 19:32 | review | Close votes | |||
| Oct 27, 2017 at 11:07 | |||||
| Oct 26, 2017 at 18:54 | history | asked | john mangual | CC BY-SA 3.0 |