2 problems

Braverman–Kazhdan's acyclicity conjecture. The object $(\pi_U)_!\Psi_{G,\rho}$ is supported on $T=B/U\subset G/U$. Equivalently, for every $g\in G-B$,

Braverman–Kazhdan's conjecture. The functor $\mathrm F_{G,\rho}$ is exact with respect to the perverse $t$-structure, and it commutes with induction functors. This conjecture conce…