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Stratifications of real vector spaces from constructible sheaves with conical microsupport

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Abstract

Interpreting the syzygy theorem for tame modules over posets in the setting of derived categories of subanalytically constructible sheaves proves two conjectures due to Kashiwara and Schapira concerning the existence of stratifications of real vector spaces that play well with sheaves having microsupport in a given cone or, equivalently, sheaves in the corresponding conic topology.

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Notes

  1. Bibliographic note: this conjecture appears in v3 (the version cited here) and earlier versions of the cited arXiv preprint. It does not appear in the published version (Kashiwara and Schapira 2018), which is v6 on the arXiv. The published version is cited where it is possible to do so, and v3 (Kashiwara and Schapira 2017) is cited otherwise.

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Acknowledgements

Pierre Schapira gave helpful comments on a draft of this paper, as did a referee. Portions of this work were funded by NSF grant DMS-1702395.

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  1. Mathematics Department, Duke University, Durham, NC, 27708, USA

    Ezra Miller

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  1. Ezra Miller
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Miller, E. Stratifications of real vector spaces from constructible sheaves with conical microsupport. J Appl. and Comput. Topology 7, 473–489 (2023). https://doi.org/10.1007/s41468-023-00112-1

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