A REMARK ON THE CATEGORY OF GRADED F-MODULES

Let R = k[x, y] be a polynomial ring over a field k of prime char-acteristic p and let E denote the injective hull of k (which is isomorphic to H2(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].