Elliptic curves over the rational numbers with semi-abelian reduction\n and two-division points

2020/05/20 by Stefan Schröer, Schröer, Stefan · 1 citation
Mathematics · Social Sciences · #Algebraic Geometry and Number Theory #Vietnamese History and Culture Studies #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2005.10025

Abstract

We classify elliptic curves over the rationals whose N 'eron model over the\nintegers is semi-abelian, with good reduction at p=2, and whose Mordell--Weil\ngroup contains an element of order two that stays non-trivial at p=2.\nFurthermore, we describe those curves where the element of order two is narrow,\nor where another element of order two exists, and also express our findings in\nterms of Deligne--Mumford stacks of pointed curves of genus one.\n

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