{"paper":{"title":"The KH-Theory of Complete Simplicial Toric Varieties and the Algebraic K-Theory of Weighted Projective Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.KT","authors_text":"Adam Massey","submitted_at":"2012-06-30T18:17:13Z","abstract_excerpt":"We show that, for a complete simplicial toric variety $X$, we can determine its homotopy $\\KH$-theory entirely in terms of the torus pieces of open sets forming an open cover of $X$. We then construct conditions under which, given two complete simplicial toric varieties, the two spectra $\\KH(X) \\otimes \\Q$ and $\\KH(Y) \\otimes \\Q$ are weakly equivalent. We apply this result to determine the rational $\\KH$-theory of weighted projective spaces. We next examine $\\K$-regularity for complete toric surfaces; in particular, we show that complete toric surfaces are $\\K_{0}$-regular. We then determine c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0123","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}