Ramification theory of reciprocity sheaves, I, Zariski-Nagata purity

TL;DR

This paper proves a Zariski-Nagata purity theorem for motivic ramification filtrations of reciprocity sheaves, extending classical class field theory tools and providing criteria for ramification in algebraic geometry.

Contribution

It generalizes the Kato-Saito reciprocity map to all reciprocity sheaves and establishes new criteria for ramification filtrations.

Findings

Proves a Zariski-Nagata purity theorem for reciprocity sheaves.

Provides cut-by-curves and cut-by-surfaces criteria for ramification.

Reproduces known theorems and introduces new results in ramification theory.

Abstract

We prove a Zariski-Nagata purity theorem for the motivic ramification filtration of a reciprocity sheaf. An important tool in the proof is a generalization of the Kato-Saito reciprocity map from geometric global class field theory to all reciprocity sheaves. As a corollary we obtain cut-by-curves and cut-by-surfaces criteria for various ramification filtrations. In some cases this reproves known theorems, in some cases we obtain new results.