PreprintarXiv licencearXiv
Multiplicativity of the perverse filtration in the SLn case
Abstract
We prove that the perverse filtration of the canonical SLn Hitchin system is multiplicative when the rank and degree are coprime. Over the elliptic locus of an even-degree twisted Hitchin system, we compare the Fourier projectors for compactified Pryms with the endoscopic correspondence. We then use the square-zero property of the variant cohomology and a parabolic Higgs moduli reduction to pass to the full canonical moduli space.
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BibTeX
@misc{wen2026multiplicativity,
title = {{Multiplicativity of the perverse filtration in the $\mathrmSL_n$ case}},
author = {Xueqing Wen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03096},
eprint = {2610.03096},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03096},
}
RIS
TY - UNPB
TI - Multiplicativity of the perverse filtration in the SL_n case
AU - Xueqing Wen
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03096
UR - https://arxiv.org/abs/2610.03096
AB - We prove that the perverse filtration of the canonical SL_n Hitchin system is multiplicative when the rank and degree are coprime. Over the elliptic locus of an even-degree twisted Hitchin system, we compare the Fourier projectors for compactified Pryms with the endoscopic correspondence. We then use the square-zero property of the variant cohomology and a parabolic Higgs moduli reduction to pass to the full canonical moduli space.
ER -