发表机构
Massachusetts Institute of Technology（麻省理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该文研究一类紧化Prym纤维化的傅里叶-向井对偶性，推广Maulik-Shen-Yin方案至叠情形，证明Hausel-Thaddeus猜想影子、Corti-Hanamura动机分解猜想及反常滤过可乘性。
AI 中文摘要
我们研究了一类紧化Prym纤维化的傅里叶-向井对偶性，该类包括椭圆点上的$\mathrm{SL}$希格斯丛模空间。这导致了Hausel-Thaddeus猜想的一个影子，证明了这些纤维化的Corti-Hanamura动机分解猜想，以及反常滤过的可乘性。我们的方法可描述为将Maulik-Shen-Yin关于紧化雅可比纤维化的方案推广到对偶阿贝尔纤维化为叠的情形。这迫使我们要超越完全支撑的情形。技术工具包括Toën引入的叠式Grothendieck-Riemann-Roch tau函子的一个新拉回恒等式，关于(Arinkin-)庞加莱层的下降结果，以及沿着Franco-Hanson-Horn-Oliveira思路对光滑和结点曲线族的Prym簇的庞加莱层的比较。
英文摘要
We study Fourier-Mukai duality for a class of compactified Prym fibrations including moduli spaces of $\mathrm{SL}$ Higgs bundles over the elliptic locus. This leads to a shadow of the Hausel-Thaddeus conjecture, proof of the Corti-Hanamura motivic decomposition conjecture for these fibrations, and multiplicativity of the perverse filtration. Our approach can be described as a generalization of the Maulik-Shen-Yin package for compactified Jacobian fibrations to the case when the dual abelian fibration is a stack. This forces us to move beyond the case of full supports. Technical tools include a new pullback identity for the stacky Grothendieck-Riemann-Roch tau functor introduced by Toën, results on descent of (Arinkin-)Poincaré sheaves, and a comparison of Poincaré sheaves of the Prym varieties of families of smooth and nodal curves along the lines of Franco-Hanson-Horn-Oliveira.
Comments85 pages, comments welcome
