Jordi Vilà Casadevall

On the semistability defect of genus-2 Jacobians with potentially good reduction

Given an Abelian variety A over Q_p^{nr} with potentially good reduction, there exist a minimal extension L / Q_p^{nr} over which A acquires good reduction. The Galois group of this extension is sometimes referred to as the image of inertia. Kraus classified the groups that arise as the image of inertia of an elliptic curve, giving a criterion to identify this group in terms of the valuation of the minimal discriminant and the reduction type. In this talk, I will discuss an ongoing project (joint with G. Jakovác, J. Martínez-Marín, A. Perez and J. Shi) where we try to develop a criterion to determine the image of inertia of the Jacobian of a genus-2 curve with potentially good reduction in terms of the cluster picture of the curve.