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fix build
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blueprint/src/chapter/ch03frey.tex

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@@ -119,7 +119,7 @@ \section{Multiplicative reduction}
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We say that the reduction is \emph{split} if the two tangent lines at the ordinary double point
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are both defined over $R/\m$, and \emph{non-split} otherwise.
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\begin{lemma}{Frey_curve_mult_reduction} If $E$ is the Frey curve $Y^2=X(X-a^\ell)(X+b^\ell)$ associated to a Frey
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\begin{lemma}\label{Frey_curve_mult_reduction} If $E$ is the Frey curve $Y^2=X(X-a^\ell)(X+b^\ell)$ associated to a Frey
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package $(a,b,c,\ell)$, and if $p$ is an odd prime
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which divides $abc$, then $E$ has multiplicative reduction at~$p$.
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\end{lemma}
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is split multiplicative iff $x-y$ is a square mod $p$. We shall not need this fact.
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\end{remark}
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\begin{lemma}{Frey_curve_mult_reduction_at_two} If $E$ is the Frey curve $Y^2=X(X-a^\ell)(X+b^\ell)$ associated to a Frey package
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\begin{lemma}\label{Frey_curve_mult_reduction_at_two} If $E$ is the Frey curve $Y^2=X(X-a^\ell)(X+b^\ell)$ associated to a Frey package
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$(a,b,c,\ell)$ then $E$ has multiplicative reduction at 2.
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\end{lemma}
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\begin{proof} Indeed, the change of variables $X=4X'$

blueprint/src/macro/common.tex

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\DeclareMathOperator{\Gal}{Gal}
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\DeclareMathOperator{\Aut}{Aut}
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\DeclareMathOperator{\GL}{GL}
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\DeclareMathOperator{\SL}{SL}
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\DeclareMathOperator{\sep}{sep}
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