Base change for Bernstein centers of depth zero principal series blocks

TL;DR

This paper constructs a base change homomorphism for Bernstein centers of depth-zero principal series blocks in unramified p-adic groups and proves the fundamental lemma, aiding the study of Shimura varieties with level structure.

Contribution

It introduces a new base change homomorphism for Bernstein centers and proves the fundamental lemma in this context, advancing the understanding of depth-zero principal series blocks.

Findings

Established the base change homomorphism for Bernstein centers.

Proved the fundamental lemma for this base change.

Applied results to Shimura varieties with level structure.

Abstract

Let $G$ be an unramified group over a $p$-adic field. This article introduces a base change homomorphism for Bernstein centers of depth-zero principal series blocks for $G$ and proves the corresponding base change fundamental lemma. This result is used in the approach to Shimura varieties with $\Gamma_1(p)$-level structure initiated by M. Rapoport and the author in [HR2].