The stable trace formula for Igusa varieties, II

TL;DR

This paper stabilizes the trace formula for Igusa varieties in characteristic p using Kaletha's theory, extending previous results to more general cases where the reductive group is quasi-split at p.

Contribution

It generalizes earlier work by stabilizing the trace formula for Igusa varieties under broader conditions using Kaletha's theory of rigid inner twists.

Findings

Stabilization of the trace formula for Igusa varieties in characteristic p.

Extension of results to quasi-split reductive groups at p.

Application of Kaletha's theory to broader cases.

Abstract

Assuming the trace formula for Igusa varieties in characteristic p, which is known by Mack-Crane in the case of Hodge type with good reduction at p, we stabilize the formula via Kaletha's theory of rigid inner twists when the reductive group in the underlying Shimura datum is quasi-split at p. This generalizes our earlier work under more restrictive hypotheses.