PreprintCC BY 4.0arXiv
Products in absolute Hodge cohomology and mixed Hodge formality
Abstract
Given a complex algebraic variety, we relate the product structure on its absolute Hodge cohomology with mixed Hodge formality, a notion of formality in the sense of rational homotopy, that takes into account the mixed Hodge structures present in complex algebraic geometry. Namely, we prove that mixed Hodge formality implies the splitting of absolute Hodge cohomology as a square-zero extension. We define and study certain products, akin to Massey products, which live in the absolute Hodge cohomology and obstruct its splitting. We also relate mixed Hodge formality to the existence of multiplicative Chow-Künneth decompositions.
Related
- Mixed Hodge structure in the cohomology of moment-angle complexes
- Generic vanishing for Dolbeault cohomology of mixed Hodge modules on abelian varieties
- Du Bois cohomology of noncommutative spaces and the Hodge numbers invariance conjecture for singular varieties
- Hodge--Deligne polynomials and Sn-representations on the cohomology of ℳ̅2,n
- Infinite free pro-p products as absolute Galois groups
BibTeX
@misc{magalhaes2026products,
title = {{Products in absolute Hodge cohomology and mixed Hodge formality}},
author = {Pedro Magalhães},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21034},
eprint = {2609.21034},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21034},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Products in absolute Hodge cohomology and mixed Hodge formality
AU - Pedro Magalhães
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.21034
UR - https://arxiv.org/abs/2609.21034
AB - Given a complex algebraic variety, we relate the product structure on its absolute Hodge cohomology with mixed Hodge formality, a notion of formality in the sense of rational homotopy, that takes into account the mixed Hodge structures present in complex algebraic geometry. Namely, we prove that mixed Hodge formality implies the splitting of absolute Hodge cohomology as a square-zero extension. We define and study certain products, akin to Massey products, which live in the absolute Hodge cohomology and obstruct its splitting. We also relate mixed Hodge formality to the existence of multiplicative Chow-Künneth decompositions.
ER -