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arXiv · 1010.5930

Cohomological Hasse principle and motivic cohomology for arithmetic schemes

Moritz Kerz·Shuji Saito
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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. 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.

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Moritz Kerz, Shuji Saito. 2010-10-28. Cohomological Hasse principle and motivic cohomology for arithmetic schemes. https://arxiv.org/abs/1010.5930

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