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

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.

Final version, accepted for publication in Crelle

References in corpus (2)

• Cancellation theorems for reciprocity sheaves
• Ramified class field theory and duality over finite fields