Publication
Title
Hochschild cohomology with support
Author
Abstract
 In this paper, we investigate the functoriality properties of map-graded Hochschild complexes. We show that the category Map of map-graded categories is naturally a stack over the category of small categories endowed with a certain Grothendieck topology of 3-covers. For a related topology of ∞-covers on the Cartesian morphisms in Map, we prove that taking map-graded Hochschild complexes defines a sheaf. From the functoriality related to injections between map-graded categories, we obtain Hochschild complexes with support. We revisit Keller's arrow category argument from this perspective, and introduce and investigate a general Grothendieck construction which encompasses both the map-graded categories associated to presheaves of algebras and certain generalized arrow categories, which together constitute a pair of complementary tools for deconstructing Hochschild complexes.
Language
English
Source (journal)
International mathematics research notices
Publication
2015
ISSN
1073-7928
1687-0247
Volume/pages
13(2015), p. 4741-4812
ISI
000359714900009
Full text (Publisher's DOI)
Full text (open access)
Full text (publisher's version - intranet only)
UAntwerpen
 Faculty/Department Research group [E?say:metaLocaldata.cgzprojectinf] HHNcdMir - Hochschild cohomology, non-commutative deformations and mirror symmetry.Algebraic deformation techniques in geometric contexts. Publication type Subject Affiliation Publications with a UAntwerp address