Conic sheaves on subanalytic sites and Laplace transform

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 \OO^t_{E_{\RP}} and \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 \OO^{t\land}_{E_{\RP}}[n] \simeq \OO^t_{E^*_{\RP}} and \OO^{w\land}_{E_{\RP}}[n] \simeq \OO^w_{E^*_{\RP}}.Comment: 36 pages, uses xy-pi

De Rham theorem for Schwartz functions on Nash manifolds

Here we simplify the proof of the de Rham theorem for Schwartz functions on affine Nash manifolds and generalize the result to the case of non affine Nash manifolds.Comment: 7 page

Sheaves on T-topologies

The aim of this paper is to give a unifying description of various constructions (subanalytic, semialgebraic, o-minimal site) using the notion of T-topology. We then study the category of T-sheaves.Comment: 31 pages, uses xy-pic, revised versio

Invariance of o-minimal cohomology with definably compact supports

In this paper we find general criteria to ensure that, in an arbitrary o-minimal structure, the o-minimal cohomology without supports and with definably compact supports of a definable space with coefficients in a sheaf is invariant in elementary extensions and in o-minimal expansions. We also prove the o-minimal analogue of Wilder's finiteness theorem in this context.Comment: 30 pages, uses xy-pi

On the homological dimension of o-minimal and subanalytic sheaves

Here we prove that the homological dimension of the category of sheaves on a topological space satisfying some suitable conditions is finite. In particular, we find conditions to bound the homological dimension of o-minimal and subanalytic sheaves.Comment: 10 pages, uses xy-pi

On definably proper maps

In this paper we work in o-minimal structures with definable Skolem functions and show that a continuous definable map between Hausdorff locally definably compact definable spaces is definably proper if and only if it is proper morphism in the category of definable spaces. We give several other characterizations of definably proper including one involving the existence of limits of definable types. We also prove the basic properties of definably proper maps and the invariance of definably proper in elementary extensions and o-minimal expansions.Comment: 33 pages. arXiv admin note: text overlap with arXiv:1401.084