Affine Hecke categories in equal and mixed characteristic

TL;DR

This paper establishes a canonical equivalence between affine Hecke categories of reductive groups over p-adic fields and their equal characteristic counterparts, advancing understanding in representation theory and algebraic geometry.

Contribution

It proves a canonical equivalence of monodromic affine Hecke categories for reductive groups over p-adic fields and equal characteristic fields, linking different characteristic settings.

Findings

Affine Hecke categories are equivalent in equal and mixed characteristic cases.

The equivalence is canonical and respects monoidal structures.

Results bridge characteristic gap in representation theory.

Abstract

For a quasi-split tamely connected reductive group G over a p-adic field, we prove that its (monodromic) affine Hecke category is canonically equivalent to its equal characteristic counterpart as monoidal categories.