# Deligne conjecture without Langlands correspondence

Let $$X$$ be a normal variety over a finite field $$F_q$$. Fix a prime number $$l$$ relatively prime to $$q$$. Let $$\sigma$$ be a irreducible lisse $$l$$-adic sheaf on $$X$$ whose determinant has finite order. It has been proved by L. Lafforgue that for every closed point $$x\in |X|$$, the roots of the polynomial $$\mathrm{det}_{\sigma}(\mathrm{Id}-yFrob_{x}^{-1})$$ are algebraic numbers of absolute value 1. Is there a proof of this statement independent of Langlands correspondence over function fields?