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Arithmetic teichmuller theory

Rastegar, A ; Sharif University of Technology | 2019

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  1. Type of Document: Article
  2. Publisher: Iranian Academic Center for Education, Culture and Research , 2019
  3. Abstract:
  4. By Grothendieck’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 the arithmetic information of these curves. The Goal of this paper is to develop an 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. © 2019 Academic Center for Education, Culture and Research TMU
  5. Keywords:
  6. Arithmetic Teichmuller theory ; Grothendieck’s anabelian conjectures ; Outer Galois representations
  7. Source: Iranian Journal of Mathematical Sciences and Informatics ; Volume 14, Issue 2 , 2019 , Pages 157-171 ; 17354463 (ISSN)
  8. URL: http://ijmsi.ir/article-1-992-en.pdf