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arXiv · 2210.17184

The Brauer-Manin obstruction for stacky curves

Tim Santens
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Abstract

We show that the Brauer-Manin obstruction is the only obstruction to strong approximation for all stacky curves over global fields with finite abelian fundamental groups. This includes all stacky curves of genus $g = \frac{1}{2}$, thus explaining a recent counterexample to the Hasse principle of Bhargava-Poonen. We will furthermore show that the elementary obstruction is the only obstruction to the integral Hasse principle for smooth proper integral models of stacky curves of genus $g < 1$. We then compute the Brauer-Manin obstruction for smooth proper integral models of stacky curves of genus $\frac{1}{2}$.

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Tim Santens. 2022-10-31. The Brauer-Manin obstruction for stacky curves. https://arxiv.org/abs/2210.17184

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