Mixed Hodge modules on stacks

Abstract

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 $6$ 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.

arXiv comment32 pages, accepted version, fixed cleveref bug

References in corpus (7)

• Weight structures vs. $t$-structures; weight filtrations, spectral sequences, and complexes (for motives and in general)
• Cycle groups for Artin stacks
• The motive of a classifying space
• The intersection motive of the moduli stack of shtukas
• The universal six-functor formalism
• Adjoint functor theorems for $\infty$-categories
• Decomposition Theorem for Perverse sheaves on Artin stacks over finite fields