Comparison theorem for nearby cycles of a morphism without slopes

TL;DR

This paper proves a comparison theorem linking algebraic and topological nearby cycles for morphisms without slopes, showing the order of iteration does not affect the outcome for such families of functions.

Contribution

It establishes the independence of iteration order in comparison isomorphisms for nearby cycles in the absence of slopes.

Findings

Comparison theorem between algebraic and topological nearby cycles.

Order independence of iteration in comparison isomorphisms.

Applicable to families of holomorphic functions without slopes.

Abstract

The goal of this article is to prove the comparison theorem between algebraic and topological nearby cycles of a morphism without slopes. We prove in particular that for a family of holomorphic functions without slopes, if we iterate comparison isomorphisms for nearby cycles of each function the result is independent of the order of iteration.