most recent 30 from http://mathoverflow.net 2013-05-22T11:40:24Z http://mathoverflow.net/feeds/question/25018 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/25018/semi-stable-model-and-neron-model-for-family-of-elliptic-curves New_to_MO 2010-05-17T15:20:42Z 2010-05-17T15:34:42Z

<p>I am looking for an "easy-to-understand" reference for Neron Models. Specifically if I have a semi-stable family of elliptic curves over $Spec {O}_K$ , with generic fibre $E_K$ and special fibre $E_k$ , then $E_k$ is an $N$-gon of $\mathbb{P}^1$'s. In this context, what is the Neron model of $E_K$? I guess what I am asking is for a geometric description of the special fibre of the Neron model for $E_K$.</p>

http://mathoverflow.net/questions/25018/semi-stable-model-and-neron-model-for-family-of-elliptic-curves/25022#25022 Pete L. Clark 2010-05-17T15:29:07Z 2010-05-17T15:34:42Z

<p>The place to look for this is Chapter 4 ("The Neron Model") of Silverman's book <em>Advanced Topics in the Arithmetic of Elliptic Curves</em>, specifically Theorem 4.6.1: the Neron model of an elliptic curve is obtained by removing the singular points from the minimal regular proper model.</p> <p>Thus in your case the connected component is a rational curve with two points removed: as a group it is $\mathbb{G}_m$, the multiplicative group. The component group here is cyclic of order $N$. </p>