Classification of the Linearly Reductive Finite Subgroup Schemes of SL2

Mitsuyasu Hashimoto

doi:10.1007/s40306-015-0145-9

Classification of the Linearly Reductive Finite Subgroup Schemes of SL₂

Mitsuyasu Hashimoto

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

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 language	English
Pages (from-to)	527-534
Number of pages	8
Journal	Acta Mathematica Vietnamica
Volume	40
Issue number	3
DOIs	https://doi.org/10.1007/s40306-015-0145-9
Publication status	Published - Sept 22 2015

Keywords

Group scheme
Invariant theory
Kleinian singularity

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1007/s40306-015-0145-9

Cite this

@article{4fb2c74900af4510b1fb11bc40c6124f,

title = "Classification of the Linearly Reductive Finite Subgroup Schemes of SL2",

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){\^G}(Formula presented.).",

keywords = "Group scheme, Invariant theory, Kleinian singularity",

author = "Mitsuyasu Hashimoto",

note = "Publisher Copyright: {\textcopyright} 2015, Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore.",

year = "2015",

month = sep,

day = "22",

doi = "10.1007/s40306-015-0145-9",

language = "English",

volume = "40",

pages = "527--534",

journal = "Acta Mathematica Vietnamica",

issn = "0251-4184",

publisher = "Springer Verlag",

number = "3",

}

TY - JOUR

T1 - Classification of the Linearly Reductive Finite Subgroup Schemes of SL2

AU - Hashimoto, Mitsuyasu

PY - 2015/9/22

Y1 - 2015/9/22

N2 - 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.).

AB - 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.).

KW - Group scheme

KW - Invariant theory

KW - Kleinian singularity

UR - http://www.scopus.com/inward/record.url?scp=84942094938&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84942094938&partnerID=8YFLogxK

U2 - 10.1007/s40306-015-0145-9

DO - 10.1007/s40306-015-0145-9

M3 - Article

AN - SCOPUS:84942094938

SN - 0251-4184

VL - 40

SP - 527

EP - 534

JO - Acta Mathematica Vietnamica

JF - Acta Mathematica Vietnamica

IS - 3

ER -