Relative subanalytic sheaves II

TL;DR

This paper introduces a simplified construction of sheaves on a relative site over a product space, removing previous restrictions on the parameter space, and studies their functorial base change properties.

Contribution

It extends previous work by removing the subanalytic structure requirement on the parameter space, making the construction more applicable for higher-dimensional parameter spaces.

Findings

Construction becomes easier for higher-dimensional parameter spaces.

Analyzes functorial properties of base change with respect to the parameter space.

Generalizes previous sheaf construction on relative sites.

Abstract

We give a new construction of sheaves on a relative site associated to a product $X\times S$ where $S$ plays the role of a parameter space, expanding the previous construction by the same authors, where the subanalytic structure on $S$ was required. Here we let this last condition fall. In this way the construction becomes much easier to apply when dimension of $S$ is bigger than one. We also study the functorial properties of base change with respect to the parameter space.