著者 Hashimoto, Mitsuyasu|
発行日 2017-01
出版物タイトル Mathematical Journal of Okayama University
59巻
1号
資料タイプ 学術雑誌論文
著者 橋本 光靖|
抄録 The purpose of this paper is to define equivariant class group of a locally Krull scheme (that is, a scheme which is locally a prime spectrum of a Krull domain) with an action of a flat group scheme, study its basic properties, and apply it to prove the finite generation of the class group of an invariant subring. In particular, we prove the following. Let k be a field, G a smooth k-group scheme of finite type, and X a quasi-compact quasi-separated locally Krull G-scheme. Assume that there is a k-scheme Z of finite type and a dominant k -morphism Z→XZ→X. Let φ:X→Yφ:X→Y be a G -invariant morphism such that OY→(φ⁎OX)GOY→(φ⁎OX)G is an isomorphism. Then Y is locally Krull. If, moreover, Cl(X)Cl(X) is finitely generated, then Cl(G,X)Cl(G,X) and Cl(Y)Cl(Y) are also finitely generated, where Cl(G,X)Cl(G,X) is the equivariant class group. In fact, Cl(Y)Cl(Y) is a subquotient of Cl(G,X)Cl(G,X). For actions of connected group schemes on affine schemes, there are similar results of Magid and Waterhouse, but our result also holds for disconnected G. The proof depends on a similar result on (equivariant) Picard groups.
キーワード Invariant theory Class group Picard group Krull ring
備考 © 2016. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
発行日 2016-08-01
出版物タイトル Journal of Algebra
459巻
出版者 ACADEMIC PRESS INC ELSEVIER SCIENCE
開始ページ 76
終了ページ 108
ISSN 0021-8693
NCID AA00692420
資料タイプ 学術雑誌論文
言語 English
OAI-PMH Set 岡山大学
著作権者 © 2016 Elsevier Inc.
論文のバージョン author
DOI 10.1016/j.jalgebra.2016.02.025
Web of Sience KeyUT 000377319700004
フルテキストURL AMV_40_3_527.pdf
著者 橋本 光靖|
抄録 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) ˆ.
キーワード Group scheme Kleinian singularity Invariant theory
備考 The final publication is available at Springer via http://dx.doi.org/10.1007/s40306-015-0145-9
発行日 2015-09
出版物タイトル Acta Mathematica Vietnamica
40巻
3号
出版者 Springer Singapore
開始ページ 527
終了ページ 534
ISSN 0251-4184
NCID AA00508328
資料タイプ 学術雑誌論文
言語 English
OAI-PMH Set 岡山大学
著作権者 © Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2015
論文のバージョン author
DOI 10.1007/s40306-015-0145-9
オフィシャル URL http://link.springer.com/article/10.1007%2Fs40306-015-0145-9|