Density of Arithmetic Representations of Function Fields

We propose a conjecture on the density of arithmetic points in deformation space representations \'etale fundamental group positive characteristic. This? has applications to cohomology theory, for example it implies Hard Lefschetz conjecture. prove tame degree two curve $\mathbb{P}^1\setminus \{0,1,\infty\}$. v2: very small typos corrected.v3: final. Publication Epiga.