Geodesic
Mixed Hodge modules on stacks
Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e175

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Using the $\infty $-categorical enhancement of mixed Hodge modules constructed by the author in a previous paper, we explain how mixed Hodge modules canonically extend to algebraic stacks, together with all the six operations and weights. We also prove that Drew’s approach to motivic Hodge modules gives an $\infty $-category that embeds fully faithfully in mixed Hodge modules, and we identify the image as mixed Hodge modules of geometric origin. 
Tubach, Swann. Mixed Hodge modules on stacks. Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e175. doi: 10.1017/fms.2025.10122
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