21. Jan 2021
Néron models of pseudo-Abelian varieties
ALGEBRAIC GEOMETRY & NUMBER THEORY SEMINAR
Datum: 21. Januar 2021 |
Sprecher: Otto Overkamp, Leibniz Universität Hannover
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.