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Algebra, Arithmetic, and Geometry pp 267–290Cite as

Exact Category of Modules of Constant Jordan Type

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Part of the book series: Progress in Mathematics ((PM,volume 269))

Summary

For a finite group scheme G, we continue our investigation of those finite-dimensional \(kG\)-modules that are of constant Jordan type. We introduce a Quillen exact category structure \({\mathcal C}(kG)\) on these modules and investigate \(K_0({\mathcal C}(kG))\). We study which Jordan types can be realized as the Jordan types of (virtual) modules of constant Jordan type. We also briefly consider thickenings of \({\mathcal C}(kG)\) inside the triangulated category \({\rm stmod}(kG)\).

2000 Mathematics Subject Classifications: 16G10, 20C20, 20G10, 16D90, 14D15, 19A31

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Notes

  1. 1.

    2Partially supported by the NSF.

  2. 2.

    4 Partially supported by NSF Grant #03000525.

  3. 3.

    D. Benson has recently shown that such a module does not exist.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Georgia, Athens, USA

    Jon F. Carlson

  2. Department of Mathematics, University of Southern California, Los Angeles, CA, 90089, USA

    Eric M. Friedlander

Authors
  1. Jon F. Carlson
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  2. Eric M. Friedlander
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Correspondence to Jon F. Carlson .

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Editors and Affiliations

  1. Department of Mathematics, Courant Institute of Math. Sciences, New York University, Mercer St. 251, New York, 10012, New York, USA

    Yuri Tschinkel

  2. Eberly College of Science, Dept. Mathematics, Pennsylvania State University, University Park, 16802, Pennsylvania, USA

    Yuri Zarhin

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Carlson, J.F., Friedlander, E.M. (2009). Exact Category of Modules of Constant Jordan Type. In: Tschinkel, Y., Zarhin, Y. (eds) Algebra, Arithmetic, and Geometry. Progress in Mathematics, vol 269. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4745-2_6

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