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

Fuente: arXiv
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Main Authors: Kazhdan, David, Polishchuk, Alexander
Format: Preprint
Published: 2026
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author Kazhdan, David
Polishchuk, Alexander
author_facet Kazhdan, David
Polishchuk, Alexander
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2601_14557
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle $L^2$-property for algebraic stacks over local non-archimedean fields
Kazhdan, David
Polishchuk, Alexander
Algebraic Geometry
Number Theory
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.
title $L^2$-property for algebraic stacks over local non-archimedean fields
topic Algebraic Geometry
Number Theory
url https://arxiv.org/abs/2601.14557