The Proportion of Failures of the Hasse Norm Principle
نویسنده
چکیده
For any number field we calculate the exact proportion of rational numbers which are everywhere locally a norm but not globally a norm from the number field.
منابع مشابه
Failure of the Hasse principle for Châtelet surfaces in characteristic 2
Given any global field k of characteristic 2, we construct a Châtelet surface over k that fails to satisfy the Hasse principle. This failure is due to a Brauer-Manin obstruction. This construction extends a result of Poonen to characteristic 2, thereby showing that the étale-Brauer obstruction is insufficient to explain all failures of the Hasse principle over a global field of any characteristic.
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Given any global field k of characteristic 2, we construct a Châtelet surface over k which fails to satisfy the Hasse principle. This failure is due to a Brauer-Manin obstruction. This construction extends a result of Poonen to characteristic 2, thereby showing that the étale-Brauer obstruction is insufficient to explain all failures of the Hasse principle over a global field of any characteris...
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