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arXiv · 1403.1324

Classification of the linearly reductive finite subgroup schemes of $SL_2$

Mitsuyasu Hashimoto
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Abstract

We classify the linearly reductive finite subgroup schemes $G$ of $SL_2=SL(V)$ over an algebraically closed field $k$ of positive characteristic, up to conjugation. As a corollary, we prove that such $G$ is in one-to-one correspondence with an isomorphism class of two-dimensional $F$-rational Gorenstein complete local rings with the coefficient field $k$ by the correspondence $G\mapsto ((\mathop{\mathrm{Sym}} V)^G)\,\hat{~}$.

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Mitsuyasu Hashimoto. 2014-03-06. Classification of the linearly reductive finite subgroup schemes of $SL_2$. https://arxiv.org/abs/1403.1324

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