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arXiv · 2609.21034

Products in absolute Hodge cohomology and mixed Hodge formality

Pedro Magalhães
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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.

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BibTeXRIS

Pedro Magalhães. 2026-09-17. Products in absolute Hodge cohomology and mixed Hodge formality. https://arxiv.org/abs/2609.21034

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