Rank varieties and $\pi$-points for elementary supergroup schemes
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- by Dave Benson, Srikanth B. Iyengar, Henning Krause and Julia Pevtsova;
- Trans. Amer. Math. Soc. Ser. B 8 (2021), 971-998
- DOI: https://doi.org/10.1090/btran/74
- Published electronically: November 17, 2021
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Abstract:
We develop a support theory for elementary supergroup schemes, over a field of positive characteristic $p\geqslant 3$, starting with a definition of a $\pi$-point generalising cyclic shifted subgroups of Carlson for elementary abelian groups and $\pi$-points of Friedlander and Pevtsova for finite group schemes. These are defined in terms of maps from the graded algebra $k[t,\tau ]/(t^p-\tau ^2)$, where $t$ has even degree and $\tau$ has odd degree. The strength of the theory is demonstrated by classifying the parity change invariant localising subcategories of the stable module category of an elementary supergroup scheme.References
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Bibliographic Information
- Dave Benson
- Affiliation: Institute of Mathematics, University of Aberdeen, King’s College, Aberdeen AB24 3UE, Scotland, United Kingdom
- MR Author ID: 34795
- ORCID: 0000-0003-4627-0340
- Srikanth B. Iyengar
- Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112
- MR Author ID: 616284
- ORCID: 0000-0001-7597-7068
- Henning Krause
- Affiliation: Fakultät für Mathematik, Universität Bielefeld, 33501 Bielefeld, Germany
- MR Author ID: 306121
- ORCID: 0000-0003-0373-9655
- Julia Pevtsova
- Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195
- MR Author ID: 697536
- Received by editor(s): August 14, 2020
- Received by editor(s) in revised form: January 13, 2021
- Published electronically: November 17, 2021
- Additional Notes: The second author was partly supported by NSF grants DMS-1700985 and DMS-2001368. The fourth author was partly supported by NSF grants DMS-1501146, DMS-1901854, and a Brian and Tiffinie Pang faculty fellowship. The authors also acknowledge the National Science Foundation under Grant No. DMS-1440140 which supported the first, second, and fourth authors while they were in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Spring 2018 semester
- © Copyright 2021 by the authors under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0)
- Journal: Trans. Amer. Math. Soc. Ser. B 8 (2021), 971-998
- MSC (2020): Primary 18G65; Secondary 18G80, 13E10, 16W55, 16T05
- DOI: https://doi.org/10.1090/btran/74
- MathSciNet review: 4340831
Dedicated: To Jon F. Carlson on his 80th birthday