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Jacobians with complex multiplication. (English) Zbl 1285.11089
Summary: We construct and study two series of curves whose Jacobians admit complex multiplication. The curves arise as quotients of Galois coverings of the projective line with Galois group metacyclic groups \( G_{q,3}\) of order \( 3q\) with \( q \equiv 1 \bmod 3\) an odd prime, and \( G_m\) of order \( 2^{m+1}\). The complex multiplications arise as quotients of double coset algebras of the Galois groups of these coverings. We work out the CM-types and show that the Jacobians are simple abelian varieties.

MSC:
11G15 Complex multiplication and moduli of abelian varieties
14K22 Complex multiplication and abelian varieties
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