English

Piecewise linear sheaves

Algebraic Geometry 2019-06-04 v3

Abstract

On a finite-dimensional real vector space, we give a microlocal characterization of (derived) piecewise linear sheaves (PL sheaves) and prove that the triangulated category of such sheaves is generated by sheaves associated with convex polyhedra. We then give a similar theorem for PL gamma-sheaves, that is, PL sheaves associated with the gamma-topology, for a closed convex polyhedral proper cone gamma. Our motivation is that convex polyhedra may be considered as building blocks for higher dimensional barcodes.

Keywords

Cite

@article{arxiv.1805.00349,
  title  = {Piecewise linear sheaves},
  author = {Masaki Kashiwara and Pierre Schapira},
  journal= {arXiv preprint arXiv:1805.00349},
  year   = {2019}
}

Comments

A few corrections, including bibliographical, with respect to the previous version. This paper is a continuation of arXiv:1705.00955. to appear at IMRN

R2 v1 2026-06-23T01:41:37.134Z