Failure of the Hasse principle for Chatelet surfaces in characteristic 2
classification
🧮 math.NT
math.AG
keywords
characteristichasseprinciplechateletfailurefieldglobalobstruction
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Given any global field k of characteristic 2, we construct a Chatelet 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 etale-Brauer obstruction is insufficient to explain all failures of the Hasse principle over a global field of any characteristic.
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