发表机构
Westlake University; Nankai University（西湖大学; 南开大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明吸引不动点处等变重数的p-部分决定整体p-主上同调挠的阶，从而解决Juteau--Williamson挠阶猜想及其局部版本。
AI 中文摘要
设\\(X\\)为具有环面作用及吸引不动点\\(x\\)的有理光滑复仿射簇。假设\\(X\setminus\{x\}\\)是\\(p\\)-光滑的，且其整体等变上同调无\\(p\\)-挠。我们证明其整体\\(p\\)-主上同调挠的阶等于\\(x\\)处等变重数的约化分子的\\(p\\)-部分。特别地，这利用Fiebig--Williamson的等变无挠性结果，解决了Juteau--Williamson的挠阶猜想及其在Schubert簇中正规切片上的局部版本。
英文摘要
Let \(X\) be a rationally smooth complex affine variety with a torus action and an attractive fixed point \(x\). Suppose that \(X\setminus\{x\}\) is \(p\)-smooth and that its integral equivariant cohomology has no \(p\)-torsion. We prove that the order of its total \(p\)-primary cohomology torsion is the \(p\)-part of the reduced numerator of the equivariant multiplicity at \(x\). In particular, this resolves the torsion-order conjecture of Juteau--Williamson and its local version for normal slices in Schubert varieties, using the equivariant torsion-freeness result of Fiebig--Williamson.
Comments16 pages, comments are welcome!
