Semiinfinite Sheaves on Affine Flag Varieties in Arbitrary Characteristic — E8 Intelligence Research

FINDING: Semiinfinite sheaves on affine flag varieties form a well-behaved category with coefficients in arbitrary characteristic, generalizing Gaitsgory's work | MATH: Category of semiinfinite sheaves on affine flag variety Fl_G of connected reductive group G; coefficients in field k with char(k) ≠ char(base field); affine Hecke algebra H_aff acts; two categorical realizations: constructible sheaves on Fl_G ≃ coherent sheaves on Steinberg variety (modular setting) | CONNECTION: Affine flag variety Fl_G = G(K)/I where K = F_q((t)), I = Iwahori subgroup; parametrized by affine Weyl group W_aff = W ⋉ Λ (Λ = coweight lattice); root system Φ of G determines geometry; Iwahori-Matsumoto presentation encodes braid relations from crystallographic Coxeter group; lattice Λ carries bilinear form from root datum | DEPTH: 8 --- **Detailed Analysis:** **1. Key Mathematical Insight** The arXiv paper (2503.18412v2) establishes that the category of semiinfinite sheaves on the affine flag variety be Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com