While I'm reading Scholze's paper "On torsion in the cohomology of locally symmetric varieties" he constructs the anticanonical tower passing through the construction of an integral model $X_{\infty}$ over $\text{Spf}\mathbb{Z}_p^{\text{cycl}}$ which is the limit along Frobenius of integral models of strict neighborhoods of the ordinary locus. Over every neighborhood we have a universal elliptic curve given by base change, as they are defined by blow up. Is there also a universal elliptic curve over the limit? How is it constructed? Is it the base change of one of the universal elliptic curve at finite level?
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