Wednesday 8 March 2017, 16:00 - 17:00 in HG03.085
Kentaro Mitsui (Kobe University)
Models of torsors under elliptic curves
Any proper smooth geometrically integral curve of genus one over a field can be given as a torsor under an elliptic curve. We study the special fibers of the minimal proper regular models of such torsors over a complete discrete valuation field. We classify the configurations of their irreducible components when the residue field is perfect. As an application, we show the existence of separable closed points of small degree on the original curves when the residue field is finite.