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Cohomological Hasse Principle for a Threefold over a Finite Field

Chapter
Part of the NATO ASI Series book series (ASIC, volume 407)

Abstract

One of the most beautiful principles in number theory is due to Hasse who proved that a division algebra over a global field which splits locally in fact splits globally. We consider the global-local principle of this kind over a higher dimensional global field. This generalization of the Hasse principle was first studied by Kato and others in the case where the base field has transcendental degree one over a global field. In this paper we treat the case where the transcendental degree is two and the characteristic of the field is positive.

Keywords

Exact Sequence Spectral Sequence Function Field Residue Field Global Field 
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Copyright information

© Springer Science+Business Media Dordrecht 1993

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of TokyoKomaba, Meguro-ku Tokyo, 153Japan

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