Title: Néron models and genus-one double ramification cycles via Picard functors
Abstract: Néron models of Jacobians are naturally described via Picard functors. Over a discrete valuation ring, this can be obtained by Raynaud's theorem via a quotient of the non-separated Picard functor. We can also present a direct approach within the separated functor Pic^0 of twisted curves. Recently Holmes extended Raynaud's approach on a base scheme of dimension greater than one and was able to provide in this way a universal Néron model over moduli of curves. This construction admits several applications (e.g. the study of limit linear series by Biesel and Holmes). It also allows a new definition of the Double Ramification locus (DR) parametrizing curves equipped with a principal divisor. In collaboration with Holmes, we compute this cycle in genus one and match the formula of Janda-Pandharipande-Pixton-Zvonkine.