AI 中文总结
本文证明混合Hodge形式性蕴含绝对Hodge上同调的平方零扩张分解，定义类似Massey积的阻碍积，并关联乘法Chow-Künneth分解。
AI 中文摘要
给定一个复代数簇，我们将其绝对Hodge上同调上的积结构与混合Hodge形式性联系起来，后者是理性同伦意义下的一种形式性概念，考虑了复代数几何中出现的混合Hodge结构。具体地，我们证明了混合Hodge形式性蕴含绝对Hodge上同调作为平方零扩张的分解。我们定义并研究了某些类似于Massey积的积，这些积存在于绝对Hodge上同调中，并阻碍其分解。我们还将混合Hodge形式性与乘法Chow-Künneth分解的存在性联系起来。
英文摘要
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.
