Year: 2026
Type: preprint
Abstract: We prove that the Hodge filtration on local cohomology is contained in the symbolic Ext filtration, and hence in the usual Ext filtration, answering a question of Mustata and Popa. Our main observation is that the Ext filtration admits a filtered-duality interpretation via Hartshorne's algebraic de Rham complex and its infinitesimal filtration. Comparing this construction with the filtered Du Bois complex yields the containment. The same mechanism proves the higher injectivity conjecture of Popa--Shen--Vo and several variants.
Source: arXiv (Cornell University)
Authors: Chen, Qianyu, Dirks, Bradley, Olano, Sebastian
Institution: University of Michigan
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213433128