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Results tagged with neron-models
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user 3847
4
votes
Accepted
Surjectivity of specialization map
Since $\dim X_s = 1$, we have $H^2(X_s, \mathcal{O}_{X_s}) = 0$. Therefore, by deformation theory every line bundle on $X_s$ extends to a line bundle on the formal scheme $\widehat{X}$ (completion alo …
- 16.1k
3
votes
Accepted
Complexification of Néron models of Abelian varieties
No. Take an abelian variety $A_0$ over $\mathbf{Q}$ and let $A = A_0\otimes K$ where $R = \mathbf{Q}[\pi]_{(\pi)}$ and $K = R[1/\pi]$. Then $K=K'$, $T'=0$, $N(A')_s^\circ = A\otimes R$. Then you are a …
- 16.1k