TY - JOUR
T1 - Arithmetic Teichmuller Theory
TT -
JF - IJMSI
JO - IJMSI
VL - 14
IS - 2
UR - http://ijmsi.ir/article-1-992-en.html
Y1 - 2019
SP - 157
EP - 171
KW - Anabelian geometry
KW - Grothendieck conjectures
KW - Huperbolic curves
KW - Outer automorphism
KW - Galois representation.
N2 - 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.
M3
ER -