论文标题
$ p = w $ susipodure $ \ mathrm {gl} _n $
The $P=W$ conjecture for $\mathrm{GL}_n$
论文作者
论文摘要
我们证明了$ p = w $ cusindure for $ \ mathrm {gl} _n $的所有等级$ n $和任意属的曲线$ g \ geq 2 $。该证明将重言式类别的强烈变态与梅利特的好奇的硬Lefschetz定理结合在一起。对于Perversity陈述，我们以早期的工作将消失的周期结构应用于Yun的全球施普林格理论，并证明了抛物线支持定理。
We prove the $P=W$ conjecture for $\mathrm{GL}_n$ for all ranks $n$ and curves of arbitrary genus $g\geq 2$. The proof combines a strong perversity result on tautological classes with the curious Hard Lefschetz theorem of Mellit. For the perversity statement, we apply the vanishing cycles constructions in our earlier work to global Springer theory in the sense of Yun, and prove a parabolic support theorem.
