Timeline for How to associate a Dirichlet character to a Tate character?
Current License: CC BY-SA 2.5
4 events
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| Jul 9, 2013 at 22:04 | comment | added | Pig | However, everywhere I looked (e.g. Hida's book you mentioned, or Kudla's article on Tate's thesis) seems to indicate that we do want to lift $\chi$ rather than $\chi^{-1}$. Did I make a mistake somewhere? Thanks! | |
| Jul 9, 2013 at 22:03 | comment | added | Pig | Sorry for bumping this old question, but I am confused. Consider a character $\chi$ on $\left(\mathbb{Z}/p\mathbb{Z}\right)^{\times}$. If we follow this construction, then when we restrict the lifted character $c$ to $c_l: \mathbb{Q}_l^{\times} \to \mathbb{C}$ for some prime $\ell \neq p$, we get $c_l(l) = \chi(l)^{-1}$. However I thought this must be $\chi(l)$ instead, for otherwise the L-function associated to the $\chi$ and $c$ seems to be different. So I would guess that we really want to lift $\chi^{-1}$ to $\hat{\mathbb{Z}}$ rather than $\chi$, so that the $L$-factor would be right. | |
| Jun 20, 2010 at 20:19 | history | edited | Rob Harron | CC BY-SA 2.5 |
add relation to group of fractional ideals prime to N
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| Jun 20, 2010 at 18:22 | history | answered | Rob Harron | CC BY-SA 2.5 |