Néron models of pseudo-Abelian varieties

Abstract: We explain Totaro's notion of pseudo-Abelian varieties and show that they admit Néron models over excellent discrete valuation rings. As a next step, we study those Néron models and generalize the notions of good reduction and semiabelian reduction to such algebraic groups. We prove that the well-known representation-theoretic criteria for good and semiabelian reduction due to Néron-Ogg-Shafarevich and Grothendieck carry over to the pseudo-Abelian case, and give examples to show that our results are the best possible in most cases.

algebraic geometrynumber theory

Audience: researchers in the topic

Algebraic Geometry and Number Theory seminar - ISTA