Néron models of pseudo-Abelian varieties

Otto Overkamp

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arXiv · 2003.03764

Néron models of pseudo-Abelian varieties

Otto Overkamp

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Abstract

We study Néron models of pseudo-Abelian varieties over excellent discrete valuation rings of equal characteristic $p>0$ 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. Finally, we study the order of the group scheme of connected components of the Néron model in the pseudo-Abelian case. Our method is able to control the $\ell$-part (for $\ell\not=p$) of this order completely, and we study the $p$-part in a particular (but still reasonably general) situation.

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Otto Overkamp. 2021-10-25. Néron models of pseudo-Abelian varieties. https://arxiv.org/abs/2003.03764

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