On the interior motive of certain Shimura varieties: the case of Hilbert-Blumenthal varieties (Q2889568)

The paper under review constructs and analyses a Hecke equivariant Chow motive for Hilbert-Blumenthal varieties associated to a fixed totally real number field \(L\). This so-called \textit{interior motive} has interior (or intersection) cohomology of Hilbert-Blumenthal varieties as its realisations. The construction is in perfect analogy with the case of classical modular forms (i.e.~Hilbert-Blumenthal varieties for \(L=\mathbb{Q}\)). In comparison to the approaches of Deligne and Scholl in the classical case, the author develops alternative strategies based on Bondarko's formalism of weight structures.