From the 1 of 9 linked papers with an AI index.
9 papers
Topology of Galois conjugate character varieties
Junliang Shen, Siqing Zhang
The paper investigates how integral structures, automorphisms, and tautological relations in the cohomology of character varieties can be used to distinguish the homotopy types of…
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 dua…
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 foll…
On generalized Beauville decompositions
Younghan Bae, Davesh Maulik, Junliang Shen +1
Motivated by the Beauville decomposition of an abelian scheme and the "Perverse = Chern" phenomenon for a compactified Jacobian fibration, we study in this paper splittings of the…
Cohomology of compactified Jacobians for locally planar integral curves
Junliang Shen
This article surveys some recent developments on the cohomology of the compactified Jacobian associated with a locally planar integral curve. Topics discussed here include the Ngô…
Algebraic cycles and Hitchin systems
Davesh Maulik, Junliang Shen, Qizheng Yin
The purpose of this paper is to study motivic aspects of the Hitchin system for . Our results include the following. (a) We prove the motivic decomposition conjectur…