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arXiv · 2410.01525

$\mathbb{A}^1$-connected stacky curves and the Brauer group of moduli of elliptic curves

Neeraj Deshmukh·Suraj Yadav
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Abstract

Given a smooth scheme X with an action by an affine algebraic group G, we give a formula to compute the Nisnevich sheaf of the motivic connected components of the quotient stack [X/G] in the case of an orbifold. We apply it to identify all the $\mathbb{A}^1$-connected stacky curves and prove the $\mathbb{A}^1$ -connectedness of the moduli stack of elliptic curves. We also prove homotopy purity for the smooth algebraic stacks and recover a computation of the Picard group of stacky orbifold curves by computing their mixed motive.

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Neeraj Deshmukh, Suraj Yadav. 2024-10-02. $\mathbb{A}^1$-connected stacky curves and the Brauer group of moduli of elliptic curves. https://arxiv.org/abs/2410.01525

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