可弱对称再ductive 群表示的同调整性
表示论
2026-01-21 v6 代数几何
摘要
本文证明了关于可弱对称再ductive 群表示所产生的商堆栈的同调整性猜想。我们的主要结果是将堆栈的同调分解为由最大丛的某些等价类 cocharacter 索引的有限维组成部分。这一分解使得能够定义与该堆栈相关的新的 enumerative 不变量，我们开始对其进行探索。
引用
@article{arxiv.2406.09218,
title = {Cohomological integrality for weakly symmetric representations of reductive groups},
author = {Lucien Hennecart},
journal= {arXiv preprint arXiv:2406.09218},
year = {2026}
}
备注
v6: 28 pages, accepted version; v5: 27pages. Many improvements following feedback. The main result now holds for weakly symmetric representations. Title adapted; v4: Abstract and introduction rewritten and exposition improved; v3: 24 pages, corrected Lemma 4.5, added Proposition 1.4; v2: fixed example section and proof of finite dimensionality; v1:22 pages, comments very welcome