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Topology of Galois conjugate character varieties

· 2026 · math.AG · DOI 10.48550/arxiv.2607.12154 · arXiv 2607.12154

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abstract

We study the interaction between integral structures, automorphisms, and tautological relations for the cohomology of character varieties. Based on this, we propose a method to detect differences in the homotopy types of Galois conjugate character varieties. As an application, we find the first example of a pair of Galois conjugate character varieties that are not homotopy equivalent, answering negatively a 2005 question of Hausel.

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Non-liftable varieties via etale cohomology rings

math.AG · 2026-07-20 · conditional · novelty 8.0

A finite-field variety whose Q_ℓ-cohomology ring has no rational form, giving a simply-connected non-liftable example via a new cohomological obstruction.

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  • Non-liftable varieties via etale cohomology rings math.AG · 2026-07-20 · conditional · none · ref 28 · internal anchor

    A finite-field variety whose Q_ℓ-cohomology ring has no rational form, giving a simply-connected non-liftable example via a new cohomological obstruction.