An analogue of holonomic \(D\)-modules on smooth varieties in positive characteristics
Let \(X\) be a smooth variety over a field \(K\) with \(\text{char} (K)= p>0\) and \(D_X\) the ring of Grothendieck differential operators on \(X\). In this paper the author defines and studies a very nice category of \(D_X\)-modules called filtration holonomic modules. This is a modification of the same-name concept introduced by the same author [\textit{R. Bögvad}, J. Algebra 173, 638-667 (1995; Zbl 0845.14014)]. The modified definition is motivated by its usefulness and stability with respect to the usual operations. He proves that this category is closed under \(D_X\)-module extensions, submodules and quotient modules and preserved by direct and inverse images and by local cohomology. Furthermore, every filtration holonomic module has a finite decomposition series.
scientific article; zbMATH DE number 1770068