A remark on the category of graded 𝐹-modules

Gray, McKinley

doi:10.1090/proc/16147

A remark on the category of graded $F$-modules
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by McKinley Gray;

Proc. Amer. Math. Soc. 151 (2023), 3663-3672

DOI: https://doi.org/10.1090/proc/16147

Published electronically: June 6, 2023

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Abstract:

Let $R=k[x,y]$ be a polynomial ring over a field $k$ of prime characteristic $p$ and let $E$ denote the injective hull of $k$ (which is isomorphic to $H^2_{(x,y)}(R)$). We prove that $E$ is not an injective object in the category of graded $F$-modules over $R$. This answers in the negative a question raised by Lyubeznik-Singh-Walther [J. Eur. Math. Soc. (JEMS) 18 (2016), pp. 2545- 2578].

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