Integral points on conic log K3 surfaces

Yonatan Harpaz (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications

Adapting a powerful method of Swinnerton-Dyer, we give explicit sufficient conditions for the existence of integral points on certain schemes which are fibered into affine conics. This includes, in particular, cases where the scheme is geometrically a smooth log K3 surface. To the knowledge of the author, this is the first family of log K3 surfaces for which such conditions are established.

Domaines: Mathématiques [math]; Géométrie algébrique [math.AG]; Théorie des nombres [math.NT]

Yonatan Harpaz. Integral points on conic log K3 surfaces. Journal of the European Mathematical Society, 2019, 21 (3), pp.627-664. ⟨10.4171/JEMS/846⟩. ⟨hal-02409194⟩