Schwartz $\kappa$-densities for the moduli stack of rank $2$ bundles on a curve over a local field

Alexander Braverman; David Kazhdan; Alexander Polishchuk

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arXiv · 2401.01037

Schwartz $\kappa$-densities for the moduli stack of rank $2$ bundles on a curve over a local field

Alexander Braverman·David Kazhdan·Alexander Polishchuk

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Abstract

Let $\rm{Bun}$ be the moduli stack of rank $2$ bundles with fixed determinant on a smooth proper curve $C$ over a local field $F$. We show how to associate with a Schwartz $\kappa$-density, for $\rm{Re}(\kappa)\ge 1/2$, a smooth function on the corresponding coarse moduli space of very stable bundles. In the non-archimedean case we also prove that the stack $\rm{Bun}$ is $\kappa$-bounded in the sense of Definition 2.10 of [arXiv:2112.08139] for any $\kappa\in\mathbb{C}$.

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BibTeX RIS

Alexander Braverman, David Kazhdan, Alexander Polishchuk. 2024-01-02. Schwartz $\kappa$-densities for the moduli stack of rank $2$ bundles on a curve over a local field. https://arxiv.org/abs/2401.01037

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