English

Conic sheaves on subanalytic sites and Laplace transform

Algebraic Geometry 2012-03-02 v2

Abstract

In this paper we give a construction of conic sheaves on a subanalytic site and we extend the Fourier-Sato transform to this framework. Let E be a n dimensional complex vector space and let E^* be its dual. As an application we construct the conic sheaves \OOE\RPt\OO^t_{E_{\RP}} and \OOE\RPw\OO^w_{E_{\RP}} of tempered and Whitney holomorphic functions respectively and we give a sheaf theoretical interpretation of the Laplace isomorphisms of Kashiwara and Schapira which give the isomorphisms in the derived category \OOE\RPt[n]\OOE\RPt\OO^{t\land}_{E_{\RP}}[n] \simeq \OO^t_{E^*_{\RP}} and \OOE\RPw[n]\OOE\RPw\OO^{w\land}_{E_{\RP}}[n] \simeq \OO^w_{E^*_{\RP}}.

Keywords

Cite

@article{arxiv.math/0505505,
  title  = {Conic sheaves on subanalytic sites and Laplace transform},
  author = {Luca Prelli},
  journal= {arXiv preprint arXiv:math/0505505},
  year   = {2012}
}

Comments

36 pages, uses xy-pic