Cohomological Hasse principle and motivic cohomology for arithmetic schemes

Moritz Kerz; Shuji Saito

doi:10.1007/s10240-011-0038-y

Moritz Kerz ¹; Shuji Saito ²

¹ Fachbereich Mathematik, Universität Duisburg-Essen Campus Essen, 45117, Essen Germany
² Interactive Research Center of Science, Graduate School of Science and Engineering, Tokyo Institute of Technology Ookayama, Meguro, Tokyo, 152-8551 Japan

Publications Mathématiques de l'IHÉS, Volume 115 (2012), pp. 123-183

Abstract

In 1985 Kazuya Kato formulated a fascinating framework of conjectures which generalizes the Hasse principle for the Brauer group of a global field to the so-called cohomological Hasse principle for an arithmetic scheme X. In this paper we prove the prime-to-characteristic part of the cohomological Hasse principle. We also explain its implications on finiteness of motivic cohomology and special values of zeta functions.

Received: 2010-12-17
Accepted: 2011-11-22
Online First: 2011-12-09
Published online: 2012-06-07

MR Zbl

DOI: 10.1007/s10240-011-0038-y

Author's affiliations:

Moritz Kerz ¹; Shuji Saito ²

¹ Fachbereich Mathematik, Universität Duisburg-Essen Campus Essen, 45117, Essen Germany
² Interactive Research Center of Science, Graduate School of Science and Engineering, Tokyo Institute of Technology Ookayama, Meguro, Tokyo, 152-8551 Japan

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Moritz Kerz; Shuji Saito. Cohomological Hasse principle and motivic cohomology for arithmetic schemes. Publications Mathématiques de l'IHÉS, Volume 115 (2012), pp. 123-183. doi: 10.1007/s10240-011-0038-y

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