Characteristic cycle and wild Lefschetz theorems

TL;DR

This paper introduces a novel approach using Beilinson's singular support and Saito's characteristic cycle to prove a version of the wild Lefschetz theorem, supported by new finiteness results for characteristic cycles.

Contribution

It presents a new method for Lefschetz questions leveraging singular support and characteristic cycles, advancing understanding of wild Lefschetz theorems.

Findings

Proved an instance of the wild Lefschetz theorem.

Established new finiteness results for characteristic cycles.

Enhanced techniques for perverse sheaves analysis.

Abstract

By relying on a new approach to Lefschetz type questions based on Beilinson's singular support and Saito's characteristic cycle, we prove an instance of the wild Lefschetz theorem envisioned by Deligne. Our main tool are new finiteness results for the characteristic cycles of perverse sheaves.