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arXiv · 2410.04677

Holonomic \'etale sheaves are constructible

Ahmed Abbes·Takeshi Saito
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Abstract

Building on Beilinson's work, ``constructible sheaves are holonomic,'' we introduce the notion of holonomicity for \'etale sheaves, without assuming a priori constructibility. Over a perfect base field, we establish the converse of Beilinson's result, showing that holonomic sheaves are indeed constructible. This can be seen as an \'etale analogue of Kashiwara's theorem on holonomic ${\mathcal D}_X$-modules.

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Ahmed Abbes, Takeshi Saito. 2024-10-07. Holonomic \'etale sheaves are constructible. https://doi.org/10.1017/s1474748026101893

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