A higher Hodge extension of the Feigin-Tsygan Theorem
Algebraic Geometry
2022-02-22 v1 K-Theory and Homology
Abstract
We show that the extended noncommutative de Rham complex of a cofibrant resolution, when completed at a certain Hodge filtration, is (reduced) quasi-isomorphic to the periodic cyclic complex, while each of its filtration piece is quasi-isomorphic to the negative cyclic complex. This extends a classical result of Feigin and Tsygan, which corresponds to the Hodge degree part of our quasi-isomorphism. This result is applied to the study of Calabi-Yau categories in \cite{Yeu1, Yeu2}.
Keywords
Cite
@article{arxiv.2202.09499,
title = {A higher Hodge extension of the Feigin-Tsygan Theorem},
author = {Wai-Kit Yeung},
journal= {arXiv preprint arXiv:2202.09499},
year = {2022}
}
Comments
14 pages. Comments welcome