Neron models are central to the study of the reduction of abelian varieties defined over number fields at primes of the rings of integers. Only recently, people have become interested in studying Neron models of abelian schemes over bases of dimension higher than 1. The main reason why Neron models are harder to study in this setting, is that they often fail to exist. In this talk I will show that the existence of a Neron model is closely related to a condition (called toric-additivity) on the action of monodromy on the l-adic Tate module of the generic fibre, for a prime l invertible on the base. |

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