= CM reciprocity theorem
{c}
= CM reciprocity
{c}
{synonym}
For a complex CM torus $\mathbb C/\mathfrak a$ and an idele $s$ of its CM field, the automorphism corresponding to $s$ by <Artin reciprocity> takes its lattice to $s^{-1}\mathfrak a$ and acts on torsion through the adelic scalar $s^{-1}$. When the curve is defined over a larger field, use the idelic norm to the CM field. Comparison with the original curve gives a scalar in the CM field, producing the <Hecke character of a CM elliptic curve>.
Back to article page
