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arXiv · 1507.00944

Test module filtrations for unit $F$-modules

Axel Stäbler
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Abstract

We extend the notion of test module filtration introduced by Blickle for Cartier modules. We then show that this naturally defines a filtration on unit $F$-modules and prove that this filtration coincides with the notion of $V$-filtration introduced by Stadnik in the cases where he proved existence of his filtration. We also show that these filtrations do not coincide in general. Moreover, we show that for a smooth morphism $f: X \to Y$ test modules are preserved under $f^!$. We also give examples to show that this is not the case if $f$ is finite flat and tamely ramified along a smooth divisor.

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Axel Stäbler. 2015-07-03. Test module filtrations for unit $F$-modules. https://arxiv.org/abs/1507.00944

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