A monodromy criterion for existence of Neron models and a result on semi-factoriality

Orecchia, G. (2018)

Doctoral Thesis

In the first part, we introduce a new condition, called toric-additivity, on a family of abelian varieties degenerating to a semi-abelian scheme over a normal crossing divisor. The condition depends only on the l-adic Tate module of the generic fibre, for a prime l invertible on S. We show that toric-additivity is strictly related to the property of existence of Neron models. In the second part, we consider the case of a family of nodal curves over a discrete valuation ring, having split singularities. We say that such a family is semi-factorial if every line bundle on the generic bre extends to a line bundle on the total space. We give a necessary and sufficient condition for semifactoriality, in terms of combinatorics of the dual graph of the special fibre.

• Neron models
• Jacobians
• Degenerations
• Line bundles

• All authors: Orecchia, G.
• Supervisor: Edixhoven, S.J.; Liu, Q.
• Co-supervisor: Holmes, D.
• Committee: Liedtke, C.; Nicaise, J.; Smit, B. de; Vaart, A.W. van der
• Qualification: Doctor (dr.)
• Awarding Institution: Mathematics, Science, Leiden University
• Date: 2018-02-27