Timeline for CM $j$-invariants in $p$-adic fields
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 26, 2016 at 4:46 | answer | added | Vesselin Dimitrov | timeline score: 7 | |
| Mar 24, 2016 at 5:04 | comment | added | nfdc23 | CM theory gives an obstruction to density as follows. Any such $j$ generates an abelian extension of an imaginary quadratic field $K\subset \overline{\mathbf{Q}}$, so if $F$ is the compositum of the finitely many quadratic extensions of $\mathbf{Q}_p$ then $J_p \subset F^{\rm{ab}}$. For $\Gamma_F := {\rm{Gal}}(\overline{\mathbf{Q}}_p/F)$, the closed set of fixed points for the (closure of the) commutator of $\Gamma_F$ is $F^{\rm{ab}}$, so anything outside $F^{\rm{ab}}$ cannot be arbitrarily approximated by such $\sigma(j)$'s. | |
| Mar 23, 2016 at 23:59 | answer | added | Pete L. Clark | timeline score: 16 | |
| Mar 23, 2016 at 22:43 | history | edited | Michael Griffin | CC BY-SA 3.0 |
fixed grammer
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| Mar 23, 2016 at 21:06 | history | asked | Michael Griffin | CC BY-SA 3.0 |