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Gröbner basics for mixed Hodge modules (1809.10473v1)
Published 27 Sep 2018 in math.RA and math.AG
Abstract: We develop a Gr\"obner basis theory for a class of algebras that generalizes both PBW-algebras and rings of differential algebras on smooth varieties. Emphasis lies on methods to compute filtrations and graded structures defined by weight vectors. The approach is tailored for bifiltered D-modules satisfying properties of mixed Hodge modules. As a key ingredient in functors of such modules our theory applies to compute the order filtration on pieces of a V-filtration.