Proof of the Deligne-Milnor conjecture

TL;DR

This paper uses advanced algebraic geometry techniques to prove the Deligne-Milnor conjecture and generalize the Bloch conductor conjecture in pure characteristic cases, advancing understanding of ramification in arithmetic schemes.

Contribution

It introduces novel applications of derived and non-commutative algebraic geometry to longstanding conjectures in arithmetic geometry.

Findings

Proof of the Deligne-Milnor conjecture

Generalization of Bloch conductor conjecture in pure characteristic

Enhanced understanding of ramification phenomena

Abstract

We apply methods of derived and non-commutative algebraic geometry to understand ramification phenomena on arithmetic schemes. As an application, we prove the Deligne-Milnor conjecture and, in the pure characteristic case, a generalization of Bloch conductor conjecture.