{"paper":{"title":"Witt, $GW$, $K$-theory of quasi-projective schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.KT"],"primary_cat":"math.AC","authors_text":"Satya Mandal","submitted_at":"2015-07-14T19:40:48Z","abstract_excerpt":"In this article we continue our investigation of the Derived Equivalences over noetherian quasi-projective schemes $X$, over affine schemes $\\spec{A}$. For integers $k\\geq 0$, let $C{\\mathbb M}^k(X)$ denote the category of coherent ${\\CO}_X$-modules ${\\mathcal F}$, with locally free dimension $proj\\dim(\\CF)=k=grade({\\mathcal F})$. We prove that there is a zig-zag equivalence ${\\mathcal D}}^b\\left(C{\\mathbb M}^k(X)\\right) \\to {\\mathcal D}^k\\left({\\mathcal V}(X)\\right)$ of the derived categories. It follows that there is a sequence of zig-zag maps ${\\mathbb K}\\left(C{\\mathbb M}^{k+1}(X)\\right) \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03978","kind":"arxiv","version":3},"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"}