Document Type
Article
Publication Date
2017
Publication Title
Quaestiones Mathematicae
DOI
10.2989/16073606.2017.1283545
ISSN
1727-933X
Abstract
We study a notion of total acyclicity for complexes of flat sheaves over a scheme. It is Zariski-local—i.e. it can be verified on any open affine covering of the scheme—and for sheaves over a quasi-compact semi-separated scheme it agrees with the categorical notion. In particular, it agrees, in their setting, with the notion studied by Murfet and Salarian for sheaves over a noetherian semi-separated scheme. As part of the study we recover, and in several cases extend the validity of, recent results on existence of covers and precovers in categories of sheaves. One consequence is the existence of an adjoint to the inclusion of these totally acyclic complexes into the homotopy category of complexes of flat sheaves.
Recommended Citation
Christensen, Lars Winther, Sergio Estrada, Alina Iacob.
2017.
"A Zariski-Local Notion of F-Total Acyclicity for Complexes of Sheaves."
Quaestiones Mathematicae, 40 (2): 197-214.
doi: 10.2989/16073606.2017.1283545
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/548
Comments
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