Cohomological Hasse principle and motivic cohomology for arithmetic schemes

Kerz, Moritz; Saito, Shuji

doi:10.1007/s10240-011-0038-y

Kerz, Moritz ¹ ; Saito, Shuji 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, Tome 115 (2012), pp. 123-183.

Résumé

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.

MR Zbl | 1 citation dans Numdam

DOI : 10.1007/s10240-011-0038-y

Affiliations des auteurs :

Kerz, Moritz ¹ ; Saito, Shuji ²

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     title = {Cohomological {Hasse} principle and motivic cohomology for arithmetic schemes},
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Kerz, Moritz; Saito, Shuji. Cohomological Hasse principle and motivic cohomology for arithmetic schemes. Publications Mathématiques de l'IHÉS, Tome 115 (2012), pp. 123-183. doi : 10.1007/s10240-011-0038-y. http://www.numdam.org/articles/10.1007/s10240-011-0038-y/

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