Filtrations on the globalization of twisted D-modules over Dedekind schemes

Abstract

In [11], we established the theory of twisted D-modules over general base schemes. In this short note, we construct a K-invariant positive exhaustive filtration on the globalization of the twisted D-module on a smooth quasi-compact K-scheme over a Dedekind scheme S obtained by the direct image of a K-equivariant twisted integrable connection along a K-equivariant closed immersion from a smooth proper K-scheme Y with K a smooth S-affine group scheme, whose pth associated graded OS-module is locally free of finite rank for every integer p. In particular, the k-module of its global sections is projective if S is affine with coordinate ring k.