Try to ask Tony.
Email from Thomas Riepe:
Conc. 1-motives, I’d recommend the appendix of Milne’s book “Arithmetic Duality Theorems” for the background on biextensions and Neron models, for biextensions probably further Mumford’s nice article and the references Milne makes. For Neron models, IMO one does not need to know the details, so Artin’s article on them in “Arithm. Geometry” may be enough (for more I’d recommend Bosch etc.‘s book).
http://mathoverflow.net/questions/416/existence-of-smooth-models
Neron model: Book by Bosch et al under Ell curves folder
nLab page on Models