**ODTÜ-B****İ****LKENT
ALGEBRAIC GEOMETRY SEM****I****NAR**

**“****Belyi’s**** Theorem - IV****”**

By

**ALİ SİNAN SERTÖZ**

**(****Bilkent****
University****)**

**Abstract: **In the previous talks, the proof of Belyi's theorem was completed modulo a finiteness
criterion. In this talk I will first remind certain concepts from last
semester's talk and then I will prove that finiteness
criterion. Namely, I will prove that a compact
Riemann surface S is defined over the algebraic numbers Q¯ if and only if the
orbit of S under the action of the Galois group Gal(C/Q) is finite. This will complete our coverage of chapter 3.

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**Date: ****Friday, February 27, 2015**

**Time: ****15.40**

**Place: ****Mathematics Seminar Room,
****SA – 141**

Tea and cookies will be served before the
seminar.