arXiv · 2306.14777
This is a review article based on a mini-course comprised of four talks given by the author at Berkeley.
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Denis Nesterov. 2023-06-26. Quasimaps to moduli spaces of sheaves and related topics. https://arxiv.org/abs/2306.14777
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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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