The stalk formula for multi-microlocal Hom functors and multi-microlocal Sato's triangle

TL;DR

This paper advances multi-microlocal sheaf theory by establishing a stalk formula for multi-microlocalized Hom functors, computing examples, and constructing the Sato's triangle within this generalized framework.

Contribution

It introduces a stalk formula for multi-microlocalized Hom functors and constructs the Sato's triangle in multi-microlocal analysis, extending existing microlocal sheaf theory.

Findings

Derived the stalk formula for multi-microlocalized Hom functors.

Computed examples illustrating multi-microlocalization.

Established the Sato's triangle in the multi-microlocal context.

Abstract

The concept of ``multi-microlocalization'' was introduced to extend the usual microlocal sheaf theory to a more general scope. This paper aims to further extend this theory by exploring advanced topics. One is a stalk formula for multi-microlocalized Hom functors and we compute some examples in multi-microlocal settings. Secondly we construct the Sato's triangle in the context of multi-microlocal analysis. Ultimately we get the Sato's triangle for the multi-microlocalized Hom functors.