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://www.numdam.org/articles/10.1007/s10240-011-0038-y/} }
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%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://www.numdam.org/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, Volume 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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