The Frobenius morphism in invariant theory II

Špela Špenko; Theo Raedschelders; Michel Van den Bergh

doi:10.1016/j.aim.2022.108587

The Frobenius morphism in invariant theory II

Špela Špenko, Theo Raedschelders, Michel Van den Bergh

Wiskunde

Onderzoeksoutput: Article › peer review

4 Citaten (Scopus)

Samenvatting

Let R be the homogeneous coordinate ring of the Grassmannian defined over an algebraically closed field of characteristic . In this paper we give a description of the decomposition of , considered as graded -module, for . This is a companion paper to our earlier paper, where the case was treated, and taken together, our results imply that has finite F-representation type (FFRT). Though it is expected that all rings of invariants for reductive groups have FFRT, ours is the first non-trivial example of such a ring for a group which is not linearly reductive. As a corollary, we show that the ring of differential operators is simple, that has global finite F-representation type (GFFRT) and that provides a noncommutative resolution for

Originele taal-2	English
Artikelnummer	108587
Aantal pagina's	64
Tijdschrift	Advances in Mathematics
Volume	410
DOI's	https://doi.org/10.1016/j.aim.2022.108587
Status	Published - 3 dec. 2022

Bibliografische nota

Funding Information:
The first author is supported by an EPSRC postdoctoral fellowship EP/R005214/1.The second author is a FWO [PEGASUS]2 Marie Skłodowska-Curie fellow at the Free University of Brussels (funded by the European Union Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 665501 with the Research Foundation Flanders (FWO)). During part of this work she was also a postdoc with Sue Sierra at the University of Edinburgh.The third author is a senior researcher at the Research Foundation Flanders (FWO). While working on this project he was supported by the FWO grant G0D8616N: “Hochschild cohomology and deformation theory of triangulated categories”.

Publisher Copyright:
© 2022

Copyright:
Copyright 2022 Elsevier B.V., All rights reserved.

Toegang tot document

10.1016/j.aim.2022.108587

Andere bestanden en links

Link naar publicatie in Scopus

Citeer dit

@article{4d8ae39ee3d84900bcfb9307ad5b60d1,

title = "The Frobenius morphism in invariant theory II",

abstract = "Let R be the homogeneous coordinate ring of the Grassmannian defined over an algebraically closed field of characteristic . In this paper we give a description of the decomposition of , considered as graded -module, for . This is a companion paper to our earlier paper, where the case was treated, and taken together, our results imply that has finite F-representation type (FFRT). Though it is expected that all rings of invariants for reductive groups have FFRT, ours is the first non-trivial example of such a ring for a group which is not linearly reductive. As a corollary, we show that the ring of differential operators is simple, that has global finite F-representation type (GFFRT) and that provides a noncommutative resolution for ",

author = "{\v S}pela {\v S}penko and Theo Raedschelders and {Van den Bergh}, Michel",

note = "Funding Information: The first author is supported by an EPSRC postdoctoral fellowship EP/R005214/1.The second author is a FWO [PEGASUS]2 Marie Sk{\l}odowska-Curie fellow at the Free University of Brussels (funded by the European Union Horizon 2020 research and innovation programme under the Marie Sk{\l}odowska-Curie grant agreement No 665501 with the Research Foundation Flanders (FWO)). During part of this work she was also a postdoc with Sue Sierra at the University of Edinburgh.The third author is a senior researcher at the Research Foundation Flanders (FWO). While working on this project he was supported by the FWO grant G0D8616N: “Hochschild cohomology and deformation theory of triangulated categories”. Publisher Copyright: {\textcopyright} 2022 Copyright: Copyright 2022 Elsevier B.V., All rights reserved.",

year = "2022",

month = dec,

day = "3",

doi = "10.1016/j.aim.2022.108587",

language = "English",

volume = "410",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - The Frobenius morphism in invariant theory II

AU - Špenko, Špela

AU - Raedschelders, Theo

AU - Van den Bergh, Michel

N1 - Funding Information: The first author is supported by an EPSRC postdoctoral fellowship EP/R005214/1.The second author is a FWO [PEGASUS]2 Marie Skłodowska-Curie fellow at the Free University of Brussels (funded by the European Union Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 665501 with the Research Foundation Flanders (FWO)). During part of this work she was also a postdoc with Sue Sierra at the University of Edinburgh.The third author is a senior researcher at the Research Foundation Flanders (FWO). While working on this project he was supported by the FWO grant G0D8616N: “Hochschild cohomology and deformation theory of triangulated categories”. Publisher Copyright: © 2022 Copyright: Copyright 2022 Elsevier B.V., All rights reserved.

PY - 2022/12/3

Y1 - 2022/12/3

N2 - Let R be the homogeneous coordinate ring of the Grassmannian defined over an algebraically closed field of characteristic . In this paper we give a description of the decomposition of , considered as graded -module, for . This is a companion paper to our earlier paper, where the case was treated, and taken together, our results imply that has finite F-representation type (FFRT). Though it is expected that all rings of invariants for reductive groups have FFRT, ours is the first non-trivial example of such a ring for a group which is not linearly reductive. As a corollary, we show that the ring of differential operators is simple, that has global finite F-representation type (GFFRT) and that provides a noncommutative resolution for

AB - Let R be the homogeneous coordinate ring of the Grassmannian defined over an algebraically closed field of characteristic . In this paper we give a description of the decomposition of , considered as graded -module, for . This is a companion paper to our earlier paper, where the case was treated, and taken together, our results imply that has finite F-representation type (FFRT). Though it is expected that all rings of invariants for reductive groups have FFRT, ours is the first non-trivial example of such a ring for a group which is not linearly reductive. As a corollary, we show that the ring of differential operators is simple, that has global finite F-representation type (GFFRT) and that provides a noncommutative resolution for

UR - http://www.scopus.com/inward/record.url?scp=85140293928&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2022.108587

DO - 10.1016/j.aim.2022.108587

M3 - Article

SN - 0001-8708

VL - 410

JO - Advances in Mathematics

JF - Advances in Mathematics

M1 - 108587

ER -

The Frobenius morphism in invariant theory II

Samenvatting

Bibliografische nota

Toegang tot document

Andere bestanden en links

Vingerafdruk

Citeer dit