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Questions tagged [neron-models]

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64 questions
Newest Active Bountied Unanswered
4 votes
1 answer
216 views

Let $p$ be an odd prime. Suppose an elliptic curve $E/\mathbb{Q}$ has reduction of type $I_n$ at $p$. Let $\mathcal{E}$ be its Néron model, and assume that the component group $\tilde{\mathcal{E}}/\...
elliptic's user avatar
  • 95
3 votes
0 answers
236 views

Let $A/K$ be an abelian variety where $K = \operatorname{Frac}(R)$ for some discrete valuation ring $R$. Let $\mathcal{A}$ be its Neron model. Assume that $A$ has potential good reduction, so that the ...
user47437's user avatar
  • 393
3 votes
1 answer
265 views

Let $S$ be a henselian DVR and $X/S$ be a flat and proper curve with $X$ being regular. Under what conditions the specialization map $Pic^0_{X/S}(S)\to Pic^0_{X/S}(Spec(k(s)))$ is surjective? Here $s\...
Nanjun Yang's user avatar
  • 1,024
2 votes
1 answer
216 views

Let $A$ be an abelian variety of dimension $g$ over the quotient field $K$ of a DVR $R$ which is a subfield of the complex field $\mathbb{C}$. Then by a result of Grothendieck, we know that there is a ...
divergent's user avatar
  • 85
1 vote
1 answer
220 views

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 $\...
user267839's user avatar
  • 4,142
2 votes
1 answer
454 views

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}...
user267839's user avatar
  • 4,142
0 votes
0 answers
175 views

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 $\...
user267839's user avatar
  • 4,142
1 vote
2 answers
425 views

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 ...
user267839's user avatar
  • 4,142
3 votes
0 answers
198 views

Given an elliptic curve $E/\mathbb{Q}_p$, it is known that the component group of the Néron model of $E$ is cyclic of order $-v(j(E))$ when $E$ has split multiplicative reduction, and in all other ...
Nathan Lowry's user avatar
  • 333
3 votes
0 answers
229 views

Let $K$ be a field which is complete with respect to a discrete valuation $v$ with ring of integers $R$ and residue field $k$. Let $A$ an abelian variety over $K$ and let $A^t$ be the dual abelian ...
Hans's user avatar
  • 3,151
4 votes
1 answer
301 views

Let $B$ a discrete valuation ring, say for simplicity with residue field of characteristic $0$, and $K$ its quotient field. Assume that I have an abelian variety $A$ over $K$ and let $A'$ be its Néron ...
Hans's user avatar
  • 3,151
0 votes
0 answers
175 views

Let $f:T_1 \to T_2$ be an isogeny of tori over a number field $K$. Does $f$ induce an isomorphism of the Lie algebras of the lft Néron models of $T_1$ and $T_2$ ? Are there some interesting properties ...
Adrien MORIN's user avatar
  • 627
1 vote
0 answers
271 views

I have a question about proof that Tamagawa number, $[E (K): E_0 (K)]$ is finite. Could you please tell (correct) me any strange parts about my understanding of the outline of the proof ? My ...
Duality's user avatar
  • 1,553
5 votes
0 answers
156 views

Let $\cal A$ be a smooth commutative group scheme over $S$, where $S$ is the spectrum of a discrete valuation ring with fraction field $K$ and residue field $k$. Suppose that $A:={\cal A}_K$ is an ...
Damian Rössler's user avatar
  • 3,346
2 votes
0 answers
202 views

Let $A$ be an abelian variety over $\mathbb{Q}_p$. Does there exist a proper flat morphism $X\to \mathrm{Spec}\:\mathbb{Z}_p$ such that the generic fiber is isomorphic to $A$, the special fiber is ...
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