FullText URL AMV_40_3_527.pdf
Author Hashimoto, Mitsuyasu|
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) ˆ.
Keywords Group scheme Kleinian singularity Invariant theory
Note The final publication is available at Springer via http://dx.doi.org/10.1007/s40306-015-0145-9
Published Date 2015-09
Publication Title Acta Mathematica Vietnamica
Volume volume40
Issue issue3
Publisher Springer Singapore
Start Page 527
End Page 534
ISSN 0251-4184
NCID AA00508328
Content Type Journal Article
language 英語
OAI-PMH Set 岡山大学
Copyright Holders © Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2015
File Version author
DOI 10.1007/s40306-015-0145-9
Official Url http://link.springer.com/article/10.1007%2Fs40306-015-0145-9|
FullText URL mjou_059_131_140.pdf
Author Hashimoto, Mitsuyasu|
Abstract 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.
Keywords canonical module symmetric algebra Frobenius algebra quasi-Frobenius algebra n-canonical module
Published Date 2017-01
Publication Title Mathematical Journal of Okayama University
Volume volume59
Issue issue1
Publisher Department of Mathematics, Faculty of Science, Okayama University
Start Page 131
End Page 140
ISSN 0030-1566
NCID AA00723502
Content Type Journal Article
language 英語
OAI-PMH Set 岡山大学
Copyright Holders Copyright©2017 by the Editorial Board of Mathematical Journal of Okayama University
File Version publisher
Related Url https://arxiv.org/abs/1609.07613
FullText URL Commun_Algebra_45_4_1509.pdf
Author Hashimoto, Mitsuyasu|
Abstract 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.
Keywords Class group descent theory Picard group principal fiber bundle
Note This is an Accepted Manuscript of an article published by Taylor & Francis Group. Fulltext available in Oct. 2017
Published Date 2016-10-07
Publication Title Communications in Algebra
Volume volume45
Issue issue4
Publisher Taylor & Francis
Start Page 1509
End Page 1532
ISSN 0092-7872
NCID AA00611371
Content Type Journal Article
language 英語
OAI-PMH Set 岡山大学
Copyright Holders https://creativecommons.org/licenses/by-nc-nd/4.0/deed.ja
File Version author
DOI 10.1080/00927872.2016.1178270
Web of Sience KeyUT 000389500800010
Related Url isVersionOf https://doi.org/10.1080/00927872.2016.1178270
FullText URL Nagoya_Math_J_226_165.pdf
Author Hashimoto, Mitsuyasu|
Abstract 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.
Note This is an Accepted Manuscript of an article published by Cambridge University Press This fulltext availavle in Dec 2017
Published Date 2017-06
Publication Title Nagoya Mathematical Journal
Volume volume226
Publisher Cambridge University Press
Start Page 165
End Page 203
ISSN 0027-7630
NCID AA00750899
Content Type Journal Article
language 英語
OAI-PMH Set 岡山大学
Copyright Holders 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.
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DOI 10.1017/nmj.2016.44
Related Url https://doi.org/10.1017/nmj.2016.44 https://arxiv.org/abs/1508.07552
Author Hashimoto, Mitsuyasu|
Abstract 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.
Keywords F-rational F-regular Dual F-signature Frobenius limit
Note This is an Accepted Manuscript of an article published by Elsevier This fulltext available in Aug 2019
Published Date 2017-08-15
Publication Title Journal of Algebra
Volume volume484
Publisher Elsevier
Start Page 207
End Page 223
ISSN 0021-8693
NCID AA00692420
Content Type Journal Article
language 英語
OAI-PMH Set 岡山大学
Copyright Holders https://creativecommons.org/licenses/by-nc-nd/4.0/deed.ja
File Version author
DOI 10.1016/j.jalgebra.2017.04.017
Web of Sience KeyUT 000403626100010
Related Url https://doi.org/10.1016/j.jalgebra.2017.04.017
FullText URL JofAlgebra_459_76.pdf
Author Hashimoto, Mitsuyasu|
Abstract 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.
Keywords Invariant theory Class group Picard group Krull ring
Note © 2016. This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Published Date 2016-08-01
Publication Title Journal of Algebra
Volume volume459
Publisher ACADEMIC PRESS INC ELSEVIER SCIENCE
Start Page 76
End Page 108
ISSN 0021-8693
NCID AA00692420
Content Type Journal Article
language 英語
OAI-PMH Set 岡山大学
Copyright Holders http://creativecommons.org/licenses/by-nc-nd/4.0/
File Version author
DOI 10.1016/j.jalgebra.2016.02.025
Web of Sience KeyUT 000377319700004
Related Url isVersionOf https://doi.org/10.1016/j.jalgebra.2016.02.025
FullText URL Adv_Math_305_144.pdf
Author Hashimoto, Mitsuyasu| Symondsb, Peter|
Abstract 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.
Keywords Frobenius direct image Hilbert–Kunz multiplicity F-signature Frobenius limit
Note This is an Accepted Manuscript of an article published by Elsevier
Published Date 2017-01-10
Publication Title Advances in Mathematics
Volume volume305
Publisher Elsevier
Start Page 144
End Page 164
ISSN 0001-8708
NCID AA00513055
Content Type Journal Article
language 英語
OAI-PMH Set 岡山大学
Copyright Holders https://creativecommons.org/licenses/by-nc-nd/4.0/deed.ja
File Version author
DOI 10.1016/j.aim.2016.09.020
Web of Sience KeyUT 000406169200003
Related Url isVersionOf https://doi.org/10.1016/j.aim.2016.09.020