D. Maulik, and J. Shen. (2022)cite arxiv:2209.02568Comment: 23 pages. Comments are welcome.
Abstract
We prove the $P=W$ conjecture for $GL_n$ for all ranks $n$ and
curves of arbitrary genus $g2$. 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.
%0 Generic
%1 maulik2022conjecture
%A Maulik, Davesh
%A Shen, Junliang
%D 2022
%K Perverse
%T The $P=W$ conjecture for $GL_n$
%U http://arxiv.org/abs/2209.02568
%X We prove the $P=W$ conjecture for $GL_n$ for all ranks $n$ and
curves of arbitrary genus $g2$. 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.
@misc{maulik2022conjecture,
abstract = {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.},
added-at = {2022-09-07T13:12:14.000+0200},
author = {Maulik, Davesh and Shen, Junliang},
biburl = {https://www.bibsonomy.org/bibtex/2bee34891cae41f1bf6cc1942ab2076e2/dragosf},
description = {The $P=W$ conjecture for $\mathrm{GL}_n$},
interhash = {75121725f9535389ceb13ba79aea3dc6},
intrahash = {bee34891cae41f1bf6cc1942ab2076e2},
keywords = {Perverse},
note = {cite arxiv:2209.02568Comment: 23 pages. Comments are welcome},
timestamp = {2022-09-07T13:12:14.000+0200},
title = {The $P=W$ conjecture for $\mathrm{GL}_n$},
url = {http://arxiv.org/abs/2209.02568},
year = 2022
}