Logarithmic good reduction and the index

Kentaro Mitsui; Arne Smeets

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arXiv · 1711.11547

Logarithmic good reduction and the index

Kentaro Mitsui·Arne Smeets

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Abstract

Let $K$ be the fraction field of a complete discrete valuation ring, with algebraically closed residue field of characteristic $p > 0$. This paper studies the index of a smooth, proper $K$-variety $X$ with logarithmic good reduction. We prove that it is prime to $p$ in `most' cases, for example if the Euler number of $X$ does not vanish, but (perhaps surprisingly) not always. We also fully characterise curves of genus $1$ with logarithmic good reduction, thereby completing classical results of T. Saito and Stix valid for curves of genus at least $2$.

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Kentaro Mitsui, Arne Smeets. 2017-11-30. Logarithmic good reduction and the index. https://arxiv.org/abs/1711.11547

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