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ID 34252
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Abstract

We present two new formulas concerning behaviors of the standard parameters of the Grothendieck-Teichmüller group GT , and discuss their relationships with classical mathematics. First, considering a non-Galois etale cover of P1 {0 1 infinity} of degree 4, we present a newtype equation satisfied by the Galois image in GT . Second, a certain equation in GL 2 (Z||Z2 ) satisfied by every element of GT is derived as an application of (profinite) free differential calculus.

Keywords
Grothendieck-Teichmüeller group
Belyi function
modular function
Note
in "Progress in Galois Theory"
(Proceedings in honor of J.Thompson's 70th birthday)
Developments in Mathematics series, Vol. 12 (2005), 123--133, Kluwer Acad. Publ
Published Date
2006-08-24
Publication Title
Developments in Mathematics
Publication Title Alternative
Progress in Galois Theory
Volume
volume12
Start Page
123
End Page
133
Content Type
Journal Article
language
英語
Refereed
True
Submission Path
algebra/1