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arXiv · 2601.14557

$L^2$-property for algebraic stacks over local non-archimedean fields

David Kazhdan·Alexander Polishchuk
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Abstract

We introduce an $L^2$-norm on the space of Schwartz half-densities over algebraic stacks over local non-archimedean fields. We show that these $L^2$-norms are finite for the stacks of $PGL_2$-bundles on $\mathbb{P}^1$ with parabolic structures at $\ge 3$ points. The latter property was conjectured in the context of the analytic Langlands correspondence of arXiv:2103.01509.

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David Kazhdan, Alexander Polishchuk. 2026-01-21. $L^2$-property for algebraic stacks over local non-archimedean fields. https://arxiv.org/abs/2601.14557

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