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Results tagged with neron-models
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user 3485
30
votes
Do all curves have Néron models
Here are some observations. I include the case $g=1$ (even if $X$ has no rational point).
Denote by $\hat{\mathcal X}$ the (proper) minimal regular model of $X$ over the $O_K$ and let $\mathcal X$ be …
- 11.1k
12
votes
Accepted
reduction of elliptic curves
The Néron model of $X$ is the smooth locus of the minimal regular model of $X$ (see Bosch-Lütkebohmert-Raynaud: Néron models, §1.5). The equivalence is then clear using the classification of Kodaira-N …
- 11.1k
11
votes
Are there Néron models over higher dimensional base schemes?
This is not answer to the OP, but to the remark of Pete on singular base scheme $S$. Here is an example explainning why one should assume regularity even in dimension $1$.
Let $T$ be a smooth curve …
- 11.1k
7
votes
Accepted
de jong's alteration theorem for families
Theorem 5.9 in de Jong's paper is pretty general ($S$ need not be local, only excellent integral of finite dimension) with $X$ proper over $S$. If $X$ is only of finite type over $S$ but separated, us …
- 11.1k
5
votes
Torsion of an abelian variety under reduction.
To complete Pete and Milne's answers when A is not an abelian scheme (for example, when it is the Néron model of an abelian variety over ${\mathbb Q}_p$ with not necessary good reduction), then for an …
- 11.1k