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We know that the Jacobian of an algebraic curve play an important role in the study of curves. My question is: Is there a "Jacobian" for an arithmetic curve such as $Spec Z$, which parameterizes some special objects on this curve. I am not an expert. Maybe my question is trivial.

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    $\begingroup$ Of course, there is the class group. This can be extended to the Arakelov Picard group. See Szpiro's article in Astérisque 127 or Neukirch's book on Algebraic Number Theory. $\endgroup$
    – Felipe Voloch
    Commented Dec 3, 2012 at 13:44
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    $\begingroup$ Thank you. Can you give me more details? $\endgroup$
    – Diego Maradona
    Commented Dec 4, 2012 at 9:50

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