Semi-stable model and Neron model for family of elliptic curves - MathOverflow 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 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 Answer by Pete L. Clark for Semi-stable model and Neron model for family of elliptic curves 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>