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Néron models of pseudo-Abelian varieties

ALGEBRAIC GEOMETRY & NUMBER THEORY SEMINAR

Date: Thursday, January 21, 2021 14:00 - 15:00
Speaker: Otto Overkamp (Leibniz Universität Hannover)
Location: https://mathseminars.org/seminar/AGNTISTA
Series: Mathematics and CS Seminar
Host: Tim Browning

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.


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