0PAH Lemma 7.3.24. Let q:Z^→Zq:\hat{Z}\to Z be the non-singular cover of ZZ. The map qq induces a bijection ∐ζ^i∈q−1(ζi)I(ζ^1,ζ2^)→∼I(ζ1,ζ2).\coprod_{\hat{\zeta}_{i}\in q^{-1}(\zeta_{i})}I(\hat{\zeta}_{1},\hat{\zeta_{2}})\mathrel{\mathop{\kern 0.0pt\to}\limits^{\sim}}I(\zeta_{1},\zeta_{2}).