Rızacan Çiloğlu | Searcharxiv

arXiv2026

Parahoric motivic Hecke categories in equal and mixed characteristic

We study constructible $\mathbb{Z}[\tfrac{1}{p}]$-linear étale motives on parahoric Hecke stacks associated with quasi-split tamely ramified reductive groups. We prove a canonical equivalence between their equal-characteristic and Witt-vector incarnations that is monoidal with respect to convolution. This extends Bando's comparison, which concerns split reductive groups and constructible étale sheaves. The proof combines the study of a family of affine Grassmannians for Pappas--Zhu group schemes with the use of the motivic nearby cycles functor.

math.AG↗

arXiv2024

Perverse sheaves on twisted affine flag varieties and Langlands duality

We provide a description of Iwahori-Whittaker equivariant perverse sheaves on affine flag varieties associated to tamely ramified reductive groups, in terms of Langlands dual data. This extends the work of Arkhipov-Bezrukavnikov from the case of split reductive groups. To achieve this, we first extend the theory of Wakimoto sheaves to our context and prove convolution exact central objects admit a filtration by such. We then establish the tilting property of the Iwahori-Whittaker averaging of certain central objects arising from the geometric Satake equivalence, which enables us to address the absence of an appropriate analogue of Gaitsgory's central functor for non-split groups.

math.RT↗