对偶边界复数的积分同调是动机性的

Tao Su
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引用次数: 0

摘要

在本论文中,我们给出了光滑准投影复代数变量的对偶边界复数的积分同调的动机特征。作为推论,任何稳定仿射空间(正维度)的对偶边界复数都是可收缩的。在另一篇论文[Su23]中,作者利用这个推论证明了在任何穿透黎曼曲面上的非常通用的 $GL_n(\mathbb{C})$ 特征变体的弱几何 P=W 猜想。
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Integral cohomology of dual boundary complexes is motivic
In this note, we give a motivic characterization of the integral cohomology of dual boundary complexes of smooth quasi-projective complex algebraic varieties. As a corollary, the dual boundary complex of any stably affine space (of positive dimension) is contractible. In a separate paper [Su23], this corollary has been used by the author in his proof of the weak geometric P=W conjecture for very generic $GL_n(\mathbb{C})$-character varieties over any punctured Riemann surfaces.
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