Failure of the Hasse principle for Enriques surfaces

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• 作者：Anthony Vá ; rilly-Alvarado^a ; ^{varilly@rice.edu} ; ; Bianca Viray^b ; ^{bviray@math.brown.edu} ;
• 关键词：Hasse principle ; Enriques surface ; É ; tale-Brauer ; K3 surface ; Transcendental obstruction ; Brauer– ; Manin
• 刊名：Advances in Mathematics
• 出版年：2011
• 出版时间：1 April 2011
• 年：2011
• 卷：226
• 期：6
• 页码：4884-4901
• 全文大小：202 K

文摘

We construct an Enriques surface X over with empty étale-Brauer set (and hence no rational points) for which there is no algebraic Brauer–Manin obstruction to the Hasse principle. In addition, if there is a transcendental obstruction on X, then we obtain a K3 surface that has a transcendental obstruction to the Hasse principle.