Cohomological Hasse principle and motivic cohomology for arithmetic schemes

By M. Kerz, S. Saito. Publications mathématiques (Bures-sur-Yvette), 2010

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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.

Subfields: Geometry and Topology, Mathematical Physics

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