|
Title
|
|
|
|
The Gerstenhaber-Schack complex for prestacks
|
|
|
Author
|
|
|
|
|
|
|
Abstract
|
|
|
|
| The aim of this work is to construct a complex which through its higher structure directly controlls deformations of general prestacks, building on the work of Gerstenhaber and Schack for presheaves of algebras. In defining a Gerstenhaber-Schack complex C-GS(.) (A) for an arbitrary prestack A, we have to introduce a differential with an infinite sequence of components instead of just two as in the presheaf case. If (A)over-bar denotes the Grothendieck construction of A, which is a U-graded category, we explicitly construct inverse quasi-isomorphisms F and G between C-GS(.) (A) and the Hochschild complex C-u((A)over-bar), as well as a concrete homotopy T : FG -> 1, which had not been obtained even in the presheaf case. As a consequence, by applying the Homotopy Transfer Theorem, one can transfer the dg Lie structure present on the Hochschild complex in order to obtain an L-infinity-structure on C-GS(.) (A), which controlls the higher deformation theory of the prestack A. This answers the open problem about the higher structure on the Gerstenhaber-Schack complex at once in the general prestack case. (C) 2018 Elsevier Inc. All rights reserved. |
|
|
|
Language
|
|
|
|
English
|
|
|
Source (journal)
|
|
|
|
Advances in mathematics. - New York, N.Y.
|
|
|
Publication
|
|
|
|
New York, N.Y.
:
2018
|
|
|
ISSN
|
|
|
|
0001-8708
|
|
|
DOI
|
|
|
|
10.1016/J.AIM.2018.02.023
|
|
|
Volume/pages
|
|
|
|
330
(2018)
, p. 173-228
|
|
|
ISI
|
|
|
|
000431472100007
|
|
|
Full text (Publisher's DOI)
|
|
|
|
|
|
|
Full text (open access)
|
|
|
|
|
|
|
Full text (publisher's version - intranet only)
|
|
|
|
|
|