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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 …
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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 …
user267839's user avatar
  • 6,038
2 votes
2 answers
285 views

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 …
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3 votes
1 answer
346 views

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}_{ …
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