The test function conjecture for parahoric local models

TL;DR

This paper proves the test function conjecture for local models of Shimura varieties with parahoric level structure, confirming a key prediction in the theory of automorphic forms and arithmetic geometry.

Contribution

It establishes the conjecture for parahoric local models, extending previous results to a broader class of Shimura varieties and their equal characteristic analogues.

Findings

Proof of the test function conjecture for parahoric local models

Validation of conjecture in equal characteristic cases

Advancement in understanding Shimura varieties and local models

Abstract

We prove the test function conjecture of Kottwitz and the first named author for local models of Shimura varieties with parahoric level structure, and their analogues in equal characteristic.