## A logarithmic interpretation of Edixhoven's jumps for Jacobians

### Johannes Nicaise

Let *A* be an abelian variety over a strictly henselian discretely valued field *K*. In his 1992 paper "Néron models and tame ramification", Edixhoven has constructed a filtration on the special fiber of the Néron model of *A* that measures the behaviour of the Néron model with respect to tamely ramified extensions of *K*. The filtration is indexed by rational numbers in [0,1], and if *A* is wildly ramified, it is an open problem whether the places where it jumps are always rational. I will explain how an interpretation of the filtration in terms of logarithmic geometry leads to explicit formulas for the jumps in the case where A is a Jacobian, which confirms in particular that they are rational. This is joint work with Dennis Eriksson and Lars Halvard Halle.