It is excerpt from "Algebraic Geometry Codes Basic Notions"(https://www.google.ru/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CCoQFjAA&url=http%3A%2F%2Fwww.math.umass.edu%2F~hajir%2Fm499c%2Ftvn-book.pdf&ei=CtLiUc2aAums4ATDloGoBA&usg=AFQjCNH8m6i46UGeRvF8J0nV_cMriSYSww&sig2=-doWN37rrQ2BMFnyUj3c1g&bvm=bv.48705608,d.bGE&cad=rjt) pg 190: "The fractional ideal a of the ﬁeld $\mathbb{K}$ is the same divisor $D$ written multiplicatively. Then the space $L(D)$ corresponds to a $a^{-1}$. The ideal class group $Cl_{K}$ is almost the group of $\mathbb{F}_r$-points of the Jacobian of the curve; itscardinality corresponds in fact to the product of the class number of the number ﬁeld by its regulator."

So I want to understand accurate statement. Is it true that for every curve $C$ over finite field there is number field $\mathbb{K}$ that Jacobian $C$ is isomorphic $Cl_{\mathbb{K}}$?

If is it true, how to build it number field for some curve?