Cohomological Hasse principle and motivic cohomology for arithmetic schemes

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.

arXiv comment47 pages, final version

References in corpus (2)

• Arithmetic homology and an integral version of Katos conjecture
• Étale duality for constructible sheaves on arithmetic schemes

Cited by in corpus (1)

• Finite generation conjectures for cohomology over finite fields