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Mathematics > Algebraic Geometry

arXiv:1805.07081 (math)
[Submitted on 18 May 2018 (v1), last revised 8 Jan 2020 (this version, v2)]

Title:The Test Function Conjecture for Local Models of Weil-restricted groups

Authors:Thomas J. Haines, Timo Richarz
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Abstract:We prove the test function conjecture of Kottwitz and the first named author for local models of Shimura varieties with parahoric level structure attached to Weil-restricted groups, as defined by B. Levin. Our result covers the (modified) local models attached to all connected reductive groups over $p$-adic local fields with $p\geq 5$. In addition, we give a self-contained study of relative affine Grassmannians and loop groups formed using general relative effective Cartier divisors in a relative curve over an arbitrary Noetherian affine scheme.
Comments: Minor corrections; added ยงยง7-8 on the test function conjecture for modified local models
Subjects: Algebraic Geometry (math.AG); Number Theory (math.NT)
Cite as: arXiv:1805.07081 [math.AG]
  (or arXiv:1805.07081v2 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1805.07081
Journal reference: Compositio Math. 156 (2020) 1348-1404
Related DOI: https://doi.org/10.1112/S0010437X20007162

Submission history

From: Timo Richarz [view email]
[v1] Fri, 18 May 2018 07:54:13 UTC (64 KB)
[v2] Wed, 8 Jan 2020 13:19:10 UTC (81 KB)
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