论文标题
在p = $ \ mathrm {sl} _n $的p = w supodiure
On the P=W conjecture for $\mathrm{SL}_n$
论文作者
论文摘要
令$ p $为主要数字。我们证明，$ p = w $ cumandure for $ \ mathrm {sl} _p $等效于$ p = w $ cunixture for $ \ mathrm {gl} _p $。结果，我们验证了第2属和$ \ mathrm {sl} _p $的$ p = w $ supenture。为了证明证明，我们计算了与$ \ Mathrm {sl} _p $ -Hitchin Moduli空间和$ \ Mathrm {Slrm {sl} _p $ -twisted角色品种相关的变体同胞的反向过滤和重量过滤。 最后，我们讨论了研究$ \ mathrm {sl} _n $ -Hitchin Moduli空间的障碍。
Let $p$ be a prime number. We prove that the $P=W$ conjecture for $\mathrm{SL}_p$ is equivalent to the $P=W$ conjecture for $\mathrm{GL}_p$. As a consequence, we verify the $P=W$ conjecture for genus 2 and $\mathrm{SL}_p$. For the proof, we compute the perverse filtration and the weight filtration for the variant cohomology associated with the $\mathrm{SL}_p$-Hitchin moduli space and the $\mathrm{SL}_p$-twisted character variety, relying on Gröchenig-Wyss-Ziegler's recent proof of the topological mirror conjecture by Hausel-Thaddeus. Finally we discuss obstructions of studying the cohomology of the $\mathrm{SL}_n$-Hitchin moduli space via compact hyper-Kähler manifolds.
