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Acta Mathematica Vietnamica

, Volume 40, Issue 3, pp 527–534 | Cite as

Classification of the Linearly Reductive Finite Subgroup Schemes of S L 2

  • Mitsuyasu HashimotoEmail author
Article
  • 56 Downloads

Abstract

We classify the linearly reductive finite subgroup schemes G of S L 2=S L(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 \(G\mapsto \left ((\mathrm {Sym\,}V)^{G}\right )\widehat {~}\).

Keywords

Group scheme Kleinian singularity Invariant theory 

Mathematics Subject Classification (2010)

Primary 14L15 Secondary 13A50 

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2015

Authors and Affiliations

  1. 1.Department of MathematicsOkayama UniversityOkayamaJapan

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