Regularity for elliptic pairs over C[[h]]

Abstract

We extend the results of Schapira and Schneiders on relative regularity and finiteness of elliptic pairs to the framework of $\shd[[\hbar]]$-modules and $\R$-constructible sheaves of $\C[[\h]]$-modules. We also construct a relative duality morphism for elliptic pairs in the smooth case and we prove that it is an isomorphism if the elliptic pair satisfies the finiteness criteria.