Geometric Eisenstein series I: finiteness theorems
成果类型：
Article; Early Access
署名作者：
Hamann, Linus; Hansen, David; Scholze, Peter
署名单位：
Harvard University; National University of Singapore; Max Planck Society
刊物名称：
INVENTIONES MATHEMATICAE
ISSN/ISSBN：
0020-9910; 1432-1297
DOI：
10.1007/s00222-026-01433-5
发表日期：
2026-06-08
关键词：
摘要：
We develop the theory of geometric Eisenstein series and constant term functors for & ell;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\ell $\end{document}-adic sheaves on stacks of bundles on the Fargues-Fontaine curve. In particular, we prove essentially optimal finiteness theorems for these functors, analogous to the usual finiteness properties of parabolic inductions and Jacquet modules. We also prove a geometric form of Bernstein's second adjointness theorem, generalizing the classical result and its recent extension to more general coefficient rings proved in [6]. As applications, we decompose the category of sheaves on BunG\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathrm{Bun}_{G}$\end{document} into cuspidal and Eisenstein parts, and show that the gluing functors between strata of BunG\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathrm{Bun}_{G}$\end{document} are continuous in a very strong sense.
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