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arXiv · 2111.01459

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

Kay Rülling·Shuji Saito
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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.

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Kay Rülling, Shuji Saito. 2021-11-02. Ramification theory of reciprocity sheaves, I, Zariski-Nagata purity. https://arxiv.org/abs/2111.01459

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