On the generic kernel filtration for modules of constant Jordan type |
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Authors: | Shawn Baland |
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Institution: | 1. Institute of Mathematics, University of Aberdeen, Aberdeen, AB24 3UE, UK
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Abstract: | Let ${E \cong (\mathbb{Z}/p)^2}$ be an elementary abelian p-group of rank two k an algebraically closed field of characteristic p, and let J =?J(kE). We investigate finitely generated kE-modules M of constant Jordan type and their generic kernels ${\mathfrak{K}(M)}$ . In particular, we answer a question posed by Carlson, Friedlander, and Suslin regarding whether or not the submodules ${J^{-i} \mathfrak{K}(M)}$ have constant Jordan type for all i ≥ 0. We show that this question has an affirmative answer whenever p = 3 or ${J^2 \mathfrak{K}(M) = 0}$ . We also show that this question has a negative answer in general by constructing a kE-module M of constant Jordan type for p ≥ 5 such that ${J^{-1} \mathfrak{K}(M)}$ does not have constant Jordan type. |
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