Classification of the Linearly Reductive Finite Subgroup Schemes of SL2

Research output: Contribution to journalArticle

Abstract

We classify the linearly reductive finite subgroup schemes G of SL2=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↦(SymV)Ĝ(Formula presented.).

Original languageEnglish
Pages (from-to)527-534
Number of pages8
JournalActa Mathematica Vietnamica
Volume40
Issue number3
DOIs
Publication statusPublished - Sep 22 2015

Fingerprint

Linearly
Subgroup
Isomorphism Classes
Gorenstein
Positive Characteristic
Local Ring
Conjugation
One to one correspondence
Algebraically closed
Corollary
Correspondence
Classify
Coefficient

Keywords

  • Group scheme
  • Invariant theory
  • Kleinian singularity

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Classification of the Linearly Reductive Finite Subgroup Schemes of SL2. / Hashimoto, Mitsuyasu.

In: Acta Mathematica Vietnamica, Vol. 40, No. 3, 22.09.2015, p. 527-534.

Research output: Contribution to journalArticle

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