论文标题
内窥镜分解和Hausel-Thaddeus猜想
Endoscopic decompositions and the Hausel-Thaddeus conjecture
论文作者
论文摘要
我们构建了自然运算符，连接具有不同等级和属的稳定Higgs束的模量空间的共同体，在数值专业化之后，恢复了Hausel-Thaddeus的拓扑镜像对称性，涉及$ \ Mathrm {Slrm {sl} _n $ - _n $ - 和$ \ mathrm {pgl-bund} pgl-______。这提供了对稳定的$ \ mathrm {sl} _n $ -Higgs捆绑的模量空间的完整描述，从重言式学班来捆绑，并通过p-adadic Integration通过p-adadic集成为Hausel-thaddeus Condoindure提供了新的证明。 我们的方法是使用消失的循环函数将Hitchin纤维的分解定理与扭曲的Hitchin纤维的分解定理相关联，其支撑更简单。
We construct natural operators connecting the cohomology of the moduli spaces of stable Higgs bundles with different ranks and genera which, after numerical specialization, recover the topological mirror symmetry conjecture of Hausel-Thaddeus concerning $\mathrm{SL}_n$- and $\mathrm{PGL}_n$-Higgs bundles. This provides a complete description of the cohomology of the moduli space of stable $\mathrm{SL}_n$-Higgs bundles in terms of the tautological classes, and gives a new proof of the Hausel-Thaddeus conjecture, proven recently by Gröchenig-Wyss-Ziegler via p-adic integration. Our method is to relate the decomposition theorem for the Hitchin fibration, using vanishing cycle functors, to the decomposition theorem for the twisted Hitchin fibration whose supports are simpler.
