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.

Comments

This version of the paper was obtained from arXIV.org. In order for the work to be deposited in arXIV.org, the author must have permission to distribute the work or the work must be available under the Creative Commons Attribution license, Creative Commons Attribution-Noncommercial-ShareAlike license, or Create Commons Public Domain Declaration. The publisher's final edited version of this article is available at Quaestiones Mathematicae.

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