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HASSE PRINCIPLES FOR ÉTALE MOTIVIC COHOMOLOGY

Part of: (Co)homology theory Arithmetic algebraic geometry

Published online by Cambridge University Press:  26 December 2018

THOMAS H. GEISSER Open the ORCID record for THOMAS H. GEISSER [Opens in a new window]
THOMAS H. GEISSER*
Affiliation:
Rikkyo University, Ikebukuro, Tokyo, Japan email geisser@rikkyo.ac.jp
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Abstract

We discuss the kernel of the localization map from étale motivic cohomology of a variety over a number field to étale motivic cohomology of the base change to its completions. This generalizes the Hasse principle for the Brauer group, and is related to Tate–Shafarevich groups of abelian varieties.

MSC classification

Primary: 11G35: Varieties over global fields 14F22: Brauer groups of schemes 14F42: Motivic cohomology; motivic homotopy theory
Type
Article
Information
Nagoya Mathematical Journal , Volume 236: Celebrating the 60th Birthday of Shuji Saito , December 2019 , pp. 63 - 83
Copyright
© 2018 Foundation Nagoya Mathematical Journal  

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Footnotes

Supported by JSPS Grant-in-Aid (C) 18K03258, (A) 15H02048-1.

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