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Typo in 0CEI
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aisejohan committed Jan 31, 2018
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Expand Up @@ -277,6 +277,7 @@ Amnon Yekutieli
Alex Youcis
John Yu
Felipe Zaldivar
Maciek Zdanowicz
Dingxin Zhang
Keke Zhang
Robin Zhang
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4 changes: 2 additions & 2 deletions models.tex
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Expand Up @@ -6525,7 +6525,7 @@ \section{Semistable reduction in genus at least two}
Choose a prime $\ell > 768g$ different from the characteristic of $k$.
Choose a finite separable extension $K'/K$ of
such that $C(K') \not = \emptyset$ and such that
$\Pic(C_{K'})[\ell] \cong (\mathbf{Z}/\ell \mathbf{Z})^{\oplus 2}$.
$\Pic(C_{K'})[\ell] \cong (\mathbf{Z}/\ell \mathbf{Z})^{\oplus 2g}$.
See
Algebraic Curves, Lemma \ref{curves-lemma-torsion-picard-becomes-visible}.
Let $R' \subset K'$ be the integral closure of $R$, see
Expand All @@ -6540,7 +6540,7 @@ \section{Semistable reduction in genus at least two}
$R$ is a discrete valuation ring with fraction field $K$,
$C$ is a smooth projective curve over $K$ with $H^0(C, \mathcal{O}_C) = K$,
with genus $g$, having a $K$-rational point, and with
$\Pic(C)[\ell] \cong (\mathbf{Z}/\ell \mathbf{Z})^{\oplus 2}$
$\Pic(C)[\ell] \cong (\mathbf{Z}/\ell \mathbf{Z})^{\oplus 2g}$
for some prime $\ell \geq 768g$ different from the characteristic of $k$.
We will prove that $C$ has semistable reduction.

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