著者 Hashimoto, Mitsuyasu|
抄録 Using the description of the Frobenius limit of modules over the ring of invariants under an action of a finite group on a polynomial ring over a field of characteristic p>0 developed by Symonds and the author, we give a characterization of the ring of invariants with a positive dual F-signature. Combining this result and Kemper's result on depths of the ring of invariants under an action of a permutation group, we give an example of an F-rational, but non-F-regular ring of invariants under the action of a finite group.
キーワード F-rational F-regular Dual F-signature Frobenius limit
備考 This is an Accepted Manuscript of an article published by Elsevier This fulltext available in Aug 2019
発行日 2017-08-15
出版物タイトル Journal of Algebra
484巻
出版者 Elsevier
開始ページ 207
終了ページ 223
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 https://creativecommons.org/licenses/by-nc-nd/4.0/deed.ja
論文のバージョン author
DOI 10.1016/j.jalgebra.2017.04.017
Web of Sience KeyUT 000403626100010
関連URL https://doi.org/10.1016/j.jalgebra.2017.04.017
著者 Hashimoto, Mitsuyasu|
抄録 We define canonical and -canonical modules of a module-finite algebra over a Noether commutative ring and study their basic properties. Using -canonical modules, we generalize a theorem on -syzygy by Araya and Iima which generalize a well-known theorem on syzygies by Evans and Griffith. Among others, we prove a noncommutative version of Aoyama’s theorem which states that a canonical module descends with respect to a flat local homomorphism.
備考 This is an Accepted Manuscript of an article published by Cambridge University Press This fulltext availavle in Dec 2017
発行日 2017-06
出版物タイトル Nagoya Mathematical Journal
226巻
出版者 Cambridge University Press
開始ページ 165
終了ページ 203
ISSN 0027-7630
NCID AA00750899
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 This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works.
論文のバージョン author
DOI 10.1017/nmj.2016.44
関連URL https://doi.org/10.1017/nmj.2016.44 https://arxiv.org/abs/1508.07552
著者 Hashimoto, Mitsuyasu| Symondsb, Peter|
抄録 We define the Frobenius limit of a module over a ring of prime characteristic to be the limit of the normalized Frobenius direct images in a certain Grothendieck group. When a finite group acts on a polynomial ring, we calculate this limit for all the modules over the twisted group algebra that are free over the polynomial ring; we also calculate the Frobenius limit for the restriction of these to the ring of invariants. As an application, we generalize the description of the generalized F-signature of a ring of invariants by the second author and Nakajima to the modular case.
キーワード Frobenius direct image Hilbert–Kunz multiplicity F-signature Frobenius limit
備考 This is an Accepted Manuscript of an article published by Elsevier Fulltext available in Jan 2019
発行日 2017-01-10
出版物タイトル Advances in Mathematics
305巻
出版者 Elsevier
開始ページ 144
終了ページ 164
ISSN 0001-8708
NCID AA00513055
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 https://creativecommons.org/licenses/by-nc-nd/4.0/deed.ja
論文のバージョン author
DOI 10.1016/j.aim.2016.09.020
Web of Sience KeyUT 000406169200003
関連URL https://doi.org/10.1016/j.aim.2016.09.020
フルテキストURL Commun_Algebra_45_4_1509.pdf
著者 Hashimoto, Mitsuyasu|
抄録 We prove a version of Grothendieck’s descent theorem on an ‘enriched’ principal fiber bundle, a principal fiber bundle with an action of a larger group scheme. Using this, we prove the isomorphisms of the equivariant Picard and the class groups arising from such a principal fiber bundle.
キーワード Class group descent theory Picard group principal fiber bundle
備考 This is an Accepted Manuscript of an article published by Taylor & Francis Group. Fulltext available in Oct. 2017
発行日 2016-10-07
出版物タイトル Communications in Algebra
45巻
4号
出版者 Taylor & Francis
開始ページ 1509
終了ページ 1532
ISSN 0092-7872
NCID AA00611371
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 https://creativecommons.org/licenses/by-nc-nd/4.0/deed.ja
論文のバージョン author
DOI 10.1080/00927872.2016.1178270
Web of Sience KeyUT 000389500800010
関連URL isVersionOf https://doi.org/10.1080/00927872.2016.1178270
フルテキストURL mjou_059_131_140.pdf
著者 Hashimoto, Mitsuyasu|
抄録 In this paper, we define and discuss higher-dimensional and absolute versions of symmetric, Frobenius, and quasi-Frobenius algebras. In particular, we compare these with the relative notions defined by Scheja and Storch. We also prove the validity of codimension two-argument for modules over a coherent sheaf of algebras with a 2-canonical module, generalizing a result of the author.
キーワード canonical module symmetric algebra Frobenius algebra quasi-Frobenius algebra n-canonical module
発行日 2017-01
出版物タイトル Mathematical Journal of Okayama University
59巻
1号
出版者 Department of Mathematics, Faculty of Science, Okayama University
開始ページ 131
終了ページ 140
ISSN 0030-1566
NCID AA00723502
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 Copyright©2017 by the Editorial Board of Mathematical Journal of Okayama University
論文のバージョン publisher
関連URL https://arxiv.org/abs/1609.07613
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|