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user39380
user39380

Does torsor of an elliptic curves necessarilycurve extend to a torsor of its Neron model?

Let $(S,\eta,s)$ be spectrum of a discrete valuation ring $R$. Let $E$ be an elliptic curve over $\eta$. Let $\mathcal{E}$ be the Neron model of $E$.

Is there a concrete example of an $E$-torsor (smooth genus one curve over $K$) that does not extends to an $\mathcal{E}$-torsor over $S$?

(I am not even sure in the case when $E$ has good reduction, or $\mathcal{E}$ is smooth over $S$.)

Does torsor of an elliptic curves necessarily extend to a torsor of its Neron model?

Let $(S,\eta,s)$ be spectrum of a discrete valuation ring $R$. Let $E$ be an elliptic curve over $\eta$. Let $\mathcal{E}$ be the Neron model of $E$.

Is there a concrete example of an $E$-torsor (smooth genus one curve over $K$) that does not extends to an $\mathcal{E}$-torsor over $S$?

Does torsor of an elliptic curve extend to torsor of its Neron model?

Let $(S,\eta,s)$ be spectrum of a discrete valuation ring $R$. Let $E$ be an elliptic curve over $\eta$. Let $\mathcal{E}$ be the Neron model of $E$.

Is there a concrete example of an $E$-torsor (smooth genus one curve over $K$) that does not extends to an $\mathcal{E}$-torsor over $S$?

(I am not even sure in the case when $E$ has good reduction, or $\mathcal{E}$ is smooth over $S$.)

Source Link
user39380
user39380

Does torsor of an elliptic curves necessarily extend to a torsor of its Neron model?

Let $(S,\eta,s)$ be spectrum of a discrete valuation ring $R$. Let $E$ be an elliptic curve over $\eta$. Let $\mathcal{E}$ be the Neron model of $E$.

Is there a concrete example of an $E$-torsor (smooth genus one curve over $K$) that does not extends to an $\mathcal{E}$-torsor over $S$?