{ "id": "1703.07888", "version": "v1", "published": "2017-03-22T23:51:38.000Z", "updated": "2017-03-22T23:51:38.000Z", "title": "On the structure of elliptic curves over finite extensions of $\\mathbb{Q}_p$ with additive reduction", "authors": [ "Michiel Kosters", "René Pannekoek" ], "comment": "12 pages, this is an extended version of arXiv:1211.5833 and contains some overlap", "categories": [ "math.AG", "math.NT" ], "abstract": "Let $p$ be a prime and let $K$ be a finite extension of $\\mathbb{Q}_p$. Let $E/K$ be an elliptic curve with additive reduction. In this paper, we study the topological group structure of the set of points of good reduction of $E(K)$. In particular, if $K/\\mathbb{Q}_p$ is unramified, we show how one can read off the topological group structure from the Weierstrass coefficients defining $E$.", "revisions": [ { "version": "v1", "updated": "2017-03-22T23:51:38.000Z" } ], "analyses": { "subjects": [ "14H52" ], "keywords": [ "elliptic curve", "finite extension", "additive reduction", "topological group structure", "weierstrass coefficients defining" ], "note": { "typesetting": "TeX", "pages": 12, "language": "en", "license": "arXiv", "status": "editable" } } }