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

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 $p\ge 5$. 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.

arXiv commentMinor corrections; added §§7-8 on the test function conjecture for modified local models

References in corpus (4)

• A proof of the Grothendieck-Serre conjecture on principal bundles over regular local rings containing infinite fields
• Local models for Weil-restricted groups
• Hilbert-Mumford stability on algebraic stacks and applications to $\mathcal{G}$-bundles on curves
• The Bernstein presentation for general connected reductive groups

Cited by in corpus (7)

• The intersection motive of the moduli stack of shtukas
• Smoothness of Schubert varieties in twisted affine Grassmannians
• Central elements in affine mod $p$ Hecke algebras via perverse ${\mathbb{F}}_p$-sheaves
• Integral models of moduli spaces of shtukas with deep Bruhat-Tits level structures
• The geometric Satake equivalence for integral motives
• Compatibility of semisimple local Langlands parameters with parahoric Satake parameters
• Point Counting on Igusa Varieties for function fields