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arXiv · 1204.1913

Pushout of quasi-finite and flat group schemes over a Dedekind ring

Marco Antei
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Abstract

Let $G$, $G_1$ and $G_2$ be quasi-finite and flat group schemes over a complete discrete valuation ring $R$, $\varphi_1:G\to G_1$ any morphism of $R$-group schemes and $\varphi_2:G\to G_2$ a model map. We construct the pushout $P$ of $G_1$ and $G_2$ over $G$ in the category of $R$-affine group schemes. In particular when $\varphi_1$ is a model map too we show that $P$ is still a model of the generic fibre of $G$. We also provide a short proof for the existence of cokernels and quotients of finite and flat group schemes over any Dedekind ring.

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Marco Antei. 2012-04-09. Pushout of quasi-finite and flat group schemes over a Dedekind ring. https://arxiv.org/abs/1204.1913

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