Categorification of the localized intersection product and Bloch conductor formula

TL;DR

This paper develops a categorification of the localized intersection product on arithmetic schemes and applies it to prove a generalized Bloch conductor conjecture, advancing the understanding of intersection theory and conductors in arithmetic geometry.

Contribution

It introduces a categorification framework for localized intersection products and extends the Bloch conductor conjecture to a more general setting.

Findings

Categorification of localized intersection product on arithmetic schemes.

Proof of a generalized Bloch conductor conjecture.

Enhanced understanding of intersection theory in arithmetic geometry.

Abstract

We categorify the localized intersection product on arithmetic schemes defined by Kato--Saito in \cite{katosaito04}. As an application, we prove a generalization of Bloch conductor conjecture.