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math.AG2026
Topology of Galois conjugate character varieties
Junliang Shen, Siqing Zhang
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 det…
math.AG2026
Dualizable abelian fibrations
Davesh Maulik, Junliang Shen, Qizheng Yin
In his proof of the fundamental lemma of the Langlands program, Ngô initiated the study of the decomposition theorem for abelian fibrations. When an abelian fibration admits a dual…
math.AG2026
On the Orlov conjecture for hyper-Kähler varieties via hyperholomorphic bundles
Davesh Maulik, Junliang Shen, Qizheng Yin
We study Fourier transforms induced by Markman's projectively hyperholomorphic bundles on products of hyper-Kähler varieties of -type. As applications, we prove the follo…