Néron models in high dimension: Nodal curves, Jacobians and tame base change

Poiret, T. (2020)

Doctoral Thesis

We describe certain birational modifications of nodal relative curves over a regular base of arbitrary dimension. Using these modifications, we provide criteria for the existence of Néron models of nodal curves and their Jacobians over a regular base of arbitrary dimension, and describe the Néron models explicitly when they exist. Then, we study the descent behavior of Néron models of abelian varieties under tamely ramified and surjective maps between regular schemes.

• Nodal curves
• Néron models
• Jacobians
• High dimension

• All authors: Poiret, T.
• Supervisor: Edixhoven, S.J.; Liu, Q.
• Committee: Kreutzer, M.T.; Romagny, M.; Tong, J.; Bouw, I.I.; Luijk, R.M. van; Holmes, D.S.T.
• Qualification: Doctor (dr.)
• Awarding Institution: Mathematical Institute (MI), Faculty of Science, Leiden University
• Date: 2020-10-20