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arXiv · 2401.01037

Schwartz $κ$-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 $κ$-density, for $\rm{Re}(κ)\ge 1/2$, 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 $κ$-bounded in the sense of Definition 2.10 of [arXiv:2112.08139] for any $κ\in\mathbb{C}$.

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Alexander Braverman, David Kazhdan, Alexander Polishchuk. 2024-09-09. Schwartz $κ$-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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