RT - Journal Article T1 - Arithmetic Teichmuller Theory JF - IJMSI YR - 2019 JO - IJMSI VO - 14 IS - 2 UR - http://ijmsi.ir/article-1-992-en.html SP - 157 EP - 171 K1 - Anabelian geometry K1 - Grothendieck conjectures K1 - Huperbolic curves K1 - Outer automorphism K1 - Galois representation. AB - By Grothedieck's Anabelian conjectures, Galois representations landing in outer automorphism group of the algebraic fundamental group which are associated to hyperbolic smooth curves defined over number fields encode all arithmetic information of these curves. The goal of this paper is to develope and arithmetic teichmuller theory, by which we mean, introducing arithmetic objects summarizing the arithmetic information coming from all curves of the same topological type defined over number fields. We also introduce Hecke-Teichmuller Lie algebra which plays the role of Hecke algebra in the anabelian framework. LA eng UL http://ijmsi.ir/article-1-992-en.html M3 ER -