English

Integral cohomology of dual boundary complexes is motivic

Algebraic Geometry 2024-09-02 v1

Abstract

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 GLn(C)GL_n(\mathbb{C})-character varieties over any punctured Riemann surfaces.

Keywords

Cite

@article{arxiv.2408.17301,
  title  = {Integral cohomology of dual boundary complexes is motivic},
  author = {Tao Su},
  journal= {arXiv preprint arXiv:2408.17301},
  year   = {2024}
}

Comments

8 pages; Following the anonymous referee's suggestion, the original paper arXiv:2307.16657 (v3) has been separated into two: v4 of that paper keeps the main result; this one deals with the motivic part