article published yes Jakub Löwit author e3b80ae2-eb8e-11eb-b029-9aef4a9108a0 TaHa department Arithmetic, geometry, topology and representation theory arising from the affine Grassmannian project We define a certain class of simple varieties over a field k by a constructive recipe and show how to control their (equivariant) truncating invariants. Consequently, we prove that on simple varieties: (i) if k = k and char k = p, the p-adic cyclotomic trace is an equivalence; (ii) if k = Q, the Goodwillie–Jones trace is an isomorphism in degree zero; (iii) we can control homotopy invariant K-theory KH, which is equivariantly formal and determined by its topological counterparts. Simple varieties are quite special, but encompass important singular examples appearing in geometric representation theory. We, in particular, show that both finite and affine Schubert varieties for GLn lie in this class, so all the above results hold for them. https://research-explorer.ista.ac.at/download/21751/21803/2026_IMRN_Loewit.pdf application/pdfno Oxford University Press2026 eng 1073-7928 1687-0247 2507.0939210.1093/imrn/rnag058 20267 Löwit, J. (2026). Equivariant localizing invariants of simple varieties. <i>International Mathematics Research Notices</i>. Oxford University Press. <a href="https://doi.org/10.1093/imrn/rnag058">https://doi.org/10.1093/imrn/rnag058</a> Löwit, Jakub. “Equivariant Localizing Invariants of Simple Varieties.” <i>International Mathematics Research Notices</i>, vol. 2026, no. 7, rnag058, Oxford University Press, 2026, doi:<a href="https://doi.org/10.1093/imrn/rnag058">10.1093/imrn/rnag058</a>. Löwit J. Equivariant localizing invariants of simple varieties. <i>International Mathematics Research Notices</i>. 2026;2026(7). doi:<a href="https://doi.org/10.1093/imrn/rnag058">10.1093/imrn/rnag058</a> Löwit, Jakub. “Equivariant Localizing Invariants of Simple Varieties.” <i>International Mathematics Research Notices</i>. Oxford University Press, 2026. <a href="https://doi.org/10.1093/imrn/rnag058">https://doi.org/10.1093/imrn/rnag058</a>. Löwit J. 2026. Equivariant localizing invariants of simple varieties. International Mathematics Research Notices. 2026(7), rnag058. J. Löwit, “Equivariant localizing invariants of simple varieties,” <i>International Mathematics Research Notices</i>, vol. 2026, no. 7. Oxford University Press, 2026. J. Löwit, International Mathematics Research Notices 2026 (2026). 217512026-04-19T22:07:48Z2026-05-06T06:36:25Z