Cohomological Hasse principle and motivic cohomology for arithmetic schemes
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.
@article{PMIHES_2012__115__123_0,
author = {Kerz, Moritz and Saito, Shuji},
title = {Cohomological {Hasse} principle and motivic cohomology for arithmetic schemes},
journal = {Publications Math\'ematiques de l'IH\'ES},
pages = {123--183},
publisher = {Springer-Verlag},
volume = {115},
year = {2012},
doi = {10.1007/s10240-011-0038-y},
mrnumber = {2929729},
zbl = {1263.14026},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1007/s10240-011-0038-y/}
}
TY - JOUR AU - Kerz, Moritz AU - Saito, Shuji TI - Cohomological Hasse principle and motivic cohomology for arithmetic schemes JO - Publications Mathématiques de l'IHÉS PY - 2012 SP - 123 EP - 183 VL - 115 PB - Springer-Verlag UR - http://geodesic.mathdoc.fr/articles/10.1007/s10240-011-0038-y/ DO - 10.1007/s10240-011-0038-y LA - en ID - PMIHES_2012__115__123_0 ER -
%0 Journal Article %A Kerz, Moritz %A Saito, Shuji %T Cohomological Hasse principle and motivic cohomology for arithmetic schemes %J Publications Mathématiques de l'IHÉS %D 2012 %P 123-183 %V 115 %I Springer-Verlag %U http://geodesic.mathdoc.fr/articles/10.1007/s10240-011-0038-y/ %R 10.1007/s10240-011-0038-y %G en %F PMIHES_2012__115__123_0
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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