## Hélène Esnault ; Moritz Kerz - Density of Arithmetic Representations of Function Fields

epiga:6568 - Épijournal de Géométrie Algébrique, March 7, 2022, Volume 6 - https://doi.org/10.46298/epiga.2022.6568
Density of Arithmetic Representations of Function Fields

Authors: Hélène Esnault ; Moritz Kerz

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

Volume: Volume 6
Published on: March 7, 2022
Accepted on: March 7, 2022
Submitted on: June 16, 2020
Keywords: Mathematics - Algebraic Geometry,Mathematics - Number Theory,11G99, 14G99