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arXiv · 2111.15315

Purely additive reduction of abelian varieties with torsion

Mentzelos Melistas
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Abstract

Let $\mathcal{O}_K$ be a discrete valuation ring with fraction field $K$ of characteristic $0$ and algebraically closed residue field $k$ of characteristic $p > 0$. Let $A/K$ be an abelian variety of dimension $g$ with a $K$-rational point of order $p$. In this article, we are interested in the reduction properties that $A/K$ can have. After discussing the general case, we specialize to $g=1$, and we study the possible Kodaira types that can occur.

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Mentzelos Melistas. 2021-11-30. Purely additive reduction of abelian varieties with torsion. https://arxiv.org/abs/2111.15315

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