closes #113

Author: ecpeterson

sigma.tex

@@ -1259,7 +1259,7 @@ \section{Modular forms and \texorpdfstring{\(MU[6, \infty)\)}{MU[6, oo)}--manifo
 \end{align*}
 \end{corollary}
 \begin{proof}
-Even though \(\tilde \theta\) is not a function on \(C_{\Tate}\) because of its quasiperiodicity, it does trivialize both \(\pi^* \sheaf I(0)\) for \(\pi\co \C^\times \times D \to C_{\Tate}\) and \(\sheaf I(0)\) for \((C_{\Tate})^\wedge_0\).  Moreover, the quasiperiodicities in the factors in the formula defining \(\delta^3 \tilde \theta|_{(C_{\Tate})^\wedge_0}\) cancel each other out, and the resulting function \emph{does} descend to give a trivialization of \(\Theta^3 \sheaf I(0)\).  By the unicity and continuity clauses in \Cref{GeneralizedTheta3IsTrivial}, it must give a formula expressing \(s\).
+Because it is quasiperiodic rather than periodic, \(\tilde \theta\) does not descend along \(\pi\co \C^\times \times D \to C_{\Tate}\) to give a function on \(C_{\Tate}\).  However, it does trivialize both \(\pi^* \sheaf I(0)\) and \(\sheaf I(0)\) for \((C_{\Tate})^\wedge_0\).  Moreover, the quasiperiodicities in the factors in the formula defining \(\delta^3 \tilde \theta|_{(C_{\Tate})^\wedge_0}\) cancel each other out, and the resulting function \emph{does} descend to give a trivialization of \(\Theta^3 \sheaf I(0)\).  By the unicity and continuity clauses in \Cref{GeneralizedTheta3IsTrivial}, it must give a formula expressing \(s\).
 \end{proof}
 
 \begin{definition}