Stratifications of real vector spaces from constructible sheaves with conical microsupport
arXiv:2008.00091
Abstract
Interpreting the syzygy theorem for tame modules over posets in the setting of derived categories of subanalytically constructible sheaves proves two conjectures due to Kashiwara and Schapira concerning the existence of stratifications of real vector spaces that play well with sheaves having microsupport in a given cone or, equivalently, sheaves in the corresponding conic topology.
17 pages. Supersedes portion of arXiv:1908.09750 related to conjectures by Kashiwara and Schapira. Material in arXiv:1908.09750 on homological algebra over arbitrary posets and primary decomposition in partially ordered groups now in separate manuscripts. v2: updated references. v3: added alternate "constructible conic sheaf" versions of main results (4.5, 5.1, 5.2); expositional improvements