Title of Seminar: Algebraic Geometry Preprint Seminar 2025
Title of Talk: Existence of global Néron models beyond semi-abelian varieties
Speaker: Subhadip Majumder, TIFR, Mumbai
Date: November 18, 2024
Time: 16:00:00 Hours
Venue: AG-77

Abstract: Let $S$ be an excellent Dedekind scheme with function field $K$. For a smooth connected commutative group scheme $G_K$ over $K$, it was conjectured in the book ``Néron Models" by Bosch, Lütkebohmert and Raynaud that a Néron-lift model for $G_K$ over $S$ exists if it doesn't contain $\mathbb{G}_a$. This conjecture is known to be true if $S$ is local or $char S=0$. However, if $char S=p>0$, then this is an open question. In the preprint {\tt arxiv.org/abs/2310.14567v2}, the authors showed that the conjecture holds when the residue fields of $S$ at closed points are perfect, but is false in general. In this talk, I will discuss the proof of this result.