Ramification theory of reciprocity sheaves, I: Zariski–Nagata purity

Author:

Rülling Kay1,Saito Shuji2

Affiliation:

1. Fakultät für Mathematik und Naturwissenschaften , Bergische Universität Wuppertal , Gaußstr. 20, 42119 Wuppertal , Germany

2. Graduate School of Mathematical Sciences , University of Tokyo , 3-8-1 Komaba , Tokyo 153-8941 , Japan

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Reference43 articles.

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2. M. Artin, A. Grothendieck, J. L. Verdier, P. Deligne and B. Saint-Donat, Seminar of algebraic geometry du Bois-Marie 1963–1964. Topos theory and étale cohomology of schemes (SGA 4). Vol. 1: Topos theory. Exp. I–IV, Lecture Notes in Math. 269, Springer, Berlin 1972.

3. M. Artin, A. Grothendieck, J. L. Verdier, P. Deligne and B. Saint-Donat, Seminar of algebraic geometry du Bois-Marie 1963–1964. Topos theory and étale cohomology of schemes (SGA 4). Vol. 3: Exp. IX–XIX, Lecture Notes in Math. 305, Springer, Berlin 1973.

4. F. Binda, K. Rülling and S. Saito, On the cohomology of reciprocity sheaves, Forum Math. Sigma 10 (2022), Paper No. e72.

5. F. Binda and S. Saito, Relative cycles with moduli and regulator maps, J. Inst. Math. Jussieu 18 (2019), no. 6, 1233–1293.

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