{"title":"Injectives obstruct Fourier-Mukai functors","authors":"Felix Küng","doi":"arxiv-2408.03027","DOIUrl":null,"url":null,"abstract":"We use the inclusion of injectives into the canonical heart as a replacement\nfor tilting objects in computations of the characteristic morphism. Then we\napply this construction to proofs of non-liftability of candidate\nnon-Fourier-Mukai functors, i.e.\\ functors that do not admit an\n$\\mathcal{A}_\\infty$/$\\mathrm{dg}$-lift. This approach allows explicit\ncomputation of the obstruction against an $\\mathcal{A}_\\infty$-lift. We in\nparticular observe that this computation gives for smooth degree $d>2$\nhypersurfaces an abundance of non-Fourier-Mukai functors.","PeriodicalId":501475,"journal":{"name":"arXiv - MATH - Commutative Algebra","volume":"6 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Commutative Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.03027","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We use the inclusion of injectives into the canonical heart as a replacement
for tilting objects in computations of the characteristic morphism. Then we
apply this construction to proofs of non-liftability of candidate
non-Fourier-Mukai functors, i.e.\ functors that do not admit an
$\mathcal{A}_\infty$/$\mathrm{dg}$-lift. This approach allows explicit
computation of the obstruction against an $\mathcal{A}_\infty$-lift. We in
particular observe that this computation gives for smooth degree $d>2$
hypersurfaces an abundance of non-Fourier-Mukai functors.