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Extend line bundle on regular curve to it's regular model
Let $S$ be the spectrum of an excellent discrete valuation ring with field of fractions $K$ and $C$ be a proper integral regular curve over $K$.
Assume, $C$ admits a proper regular flat model $\mathsc …
2
votes
1
answer
145
views
Extending line bundle to regular model
Let $S$ be the spectrum of an excellent discrete valuation ring with field of fractions $K$ and $C$ be a proper integral regular curve over $K$. Assume, $C$ admits a proper regular flat model $\mathsc …
2
votes
2
answers
285
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Dimension of Zariski closure of a locally closed subscheme
Let $S$ be a Dedekind scheme with function field $K=K(S)$ and $C$ a projective regular curve over $K$, so we can fix certain closed embedding $e:C \subset \mathbb{P}^n_K$.
Let compose this embedding w …
3
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1
answer
346
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Descent for étale covers of proper regular models of elliptic curves
Let $K$ be a complete (but think Henselian suffice for purposes of this question) local field of characteristic $0$ with residue field $k$ of characteristic $p>0$ and ring of integers $R=\mathcal{O}_{ …