Cohomological Hasse principle and motivic cohomology for arithmetic schemes

2010/10/28 by Moritz Kerz, Kerz, Moritz, Shuji Saito +1 · 1 citation
Mathematics · #14G10 #14G15 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1010.5930

openalex publication_date 2010/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: I

Cited by

• Finite generation conjectures for cohomology over finite fields

Related

• Hasse principles for higher-dimensional fields
• Cohomological Hasse principle for schemes over valuation rings of higher\n dimensional local fields
• Kato conjecture and motivic cohomology over finite fields
• Cohomological Hasse principle and resolution of quotient singularities
• Finite generation conjectures for cohomology over finite fields