Geodesic
Cohomological Hasse principle and motivic cohomology for arithmetic schemes
Kerz, Moritz1 ; Saito, Shuji2
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

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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.

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 
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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

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