preprint draft Tamás Hausel author 4A0666D8-F248-11E8-B48F-1D18A9856A870000-0002-9582-2634 Kamil P Rychlewicz author 85A07246-A8BF-11E9-B4FA-D9E3E5697425 GradSch department TaHa department An action of a complex reductive group G on a smooth projective variety X is regular when all regular unipotent elements in G act with finitely many fixed points. Then the complex G-equivariant cohomology ring of X is isomorphic to the coordinate ring of a certain regular fixed point scheme. Examples include partial flag varieties, smooth Schubert varieties and Bott-Samelson varieties. We also show that a more general version of the fixed point scheme allows a generalisation to GKM spaces, such as toric varieties. 2022 eng 2212.1183610.48550/arXiv.2212.11836 https://research-explorer.ista.ac.at/record/19071 https://research-explorer.ista.ac.at/record/17156 Hausel, Tamás, and Kamil P. Rychlewicz. “Spectrum of Equivariant Cohomology as a Fixed Point Scheme.” <i>ArXiv</i>, 2212.11836, doi:<a href="https://doi.org/10.48550/arXiv.2212.11836">10.48550/arXiv.2212.11836</a>. T. Hausel, K.P. Rychlewicz, ArXiv (n.d.). Hausel, T., &#38; Rychlewicz, K. P. (n.d.). Spectrum of equivariant cohomology as a fixed point scheme. <i>arXiv</i>. <a href="https://doi.org/10.48550/arXiv.2212.11836">https://doi.org/10.48550/arXiv.2212.11836</a> Hausel, Tamás, and Kamil P Rychlewicz. “Spectrum of Equivariant Cohomology as a Fixed Point Scheme.” <i>ArXiv</i>, n.d. <a href="https://doi.org/10.48550/arXiv.2212.11836">https://doi.org/10.48550/arXiv.2212.11836</a>. Hausel T, Rychlewicz KP. Spectrum of equivariant cohomology as a fixed point scheme. arXiv, 2212.11836. T. Hausel and K. P. Rychlewicz, “Spectrum of equivariant cohomology as a fixed point scheme,” <i>arXiv</i>. . Hausel T, Rychlewicz KP. Spectrum of equivariant cohomology as a fixed point scheme. <i>arXiv</i>. doi:<a href="https://doi.org/10.48550/arXiv.2212.11836">10.48550/arXiv.2212.11836</a> 171572024-06-23T15:01:27Z2026-04-07T12:55:46Z