Regularity for elliptic pairs over C[[h]]

TL;DR

This paper extends the theory of elliptic pairs to the setting of formal power series modules, establishing regularity, finiteness, and duality results that generalize previous work in the field.

Contribution

It introduces a framework for elliptic pairs over C[[h]]-modules, including new duality morphisms and finiteness conditions, broadening the scope of prior regularity results.

Findings

Extended regularity and finiteness results to $ ext{D}[[ ext{h}]]$-modules.

Constructed a relative duality morphism for elliptic pairs.

Proved the duality morphism is an isomorphism under finiteness conditions.

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.