Timeline for Explicit examples of algebraic Hecke characters with infinite image?

6 events

when toggle format	what		by	license	comment
Dec 24, 2012 at 16:36	comment	added	Jay		For complex CM fields, the your possible weights $\sigma_i/\overline\sigma_i$ are not the whole story: you gave a sublattice of index $2^d$. It's more that, for each CM type $\Phi$, i.e. a choice of one element of each $\{\sigma_i,\overline\sigma_i\}$, you can add the weight $\sum_{\sigma \in \Phi} \sigma$. (Thus your example is the difference of a CM type and its conjugate, or twice a CM type minus the norm.) Note that the Hecke characters attached to CM abelian varieties need precisely the weights $\Phi$.
Nov 19, 2012 at 21:48	vote	accept	Jonah Sinick
Nov 9, 2012 at 15:47	comment	added	David Loeffler		@xbnv: Thanks, I have edited my answer in the light of your comments.
Nov 9, 2012 at 15:47	history	edited	David Loeffler	CC BY-SA 3.0	Edits as suggested by xbnv
Nov 8, 2012 at 22:54	comment	added	user27056		Dear David: for the theorem you mention at the end, it is probably more appropriate to attribute it to both Artin and Weil (in view of comments Weil makes about this result in his paper where the result is used). It may also be worth noting that when $K$ contains no CM subfield then "maximal CM subfield" means $\mathbf{Q}$ (for the purpose of the statement of this theorem).
Nov 8, 2012 at 21:59	history	answered	David Loeffler	CC BY-SA 3.0